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Increased efforts to require party labels in Ohio races – Spectrum News 1

COLUMBUS, Ohio Theres an increased effort in Ohio to require more candidates to declare a party affiliation before putting their name on the ballot.

A recently passed law requires certain judicial candidates to make that information known, and the latest proposal out of the Statehouse wants local school board members to be added to the list.

Most voters do not pay close attention to politics, said Justin Buchler, a political science professor at Case Western Reserve University. Whether we are talking about the national level, the state or the local level. And that means they tend to look for cues in the simplest cue that voters tend to have is a party label.

Meanwhile, not everyone sees this as a benefit. Ohio Supreme Court Justice Jennifer Brunner filed a lawsuit over party labels being used in certain races. The lawsuit is centered on the new rule that requires certain judicial candidates to declare their party affiliation on the ballot. Brunner experienced the impact of party labels on the ballot first hand in 2022 when she ran against Republican Sharon Kennedy in the race for Ohio Supreme Court chief justice.

Ohio judicial code limits what candidates for elected judicial officers can say, and that puts judicial candidates in a different more restrictive place than other candidates who are running with party labels, said Jonathan Entin, Professor of Law at Case Western Reserve University.

The lawsuit claims party labels for these judicial candidates violate the First Amendment. But, political experts say its not that simple.

The concern becomes one of the First Amendment, said Atiba Ellis, a Professor of Law at Case Western Reserve University. One could, on the one hand, see that that information might be helpful to understand what a judge thinks and where they might be coming from. On the other hand, some might see this as a form of compelled speech in the sense of the government in issuing the ballot. Is labeling a candidate in a way that the candidate might not be labeled.

While constitutional law experts say a similar case could be made for local school board races. They also say the recent push to make more races partisan could be politically motivated.

Its tended to come from conservatives and republicans who have been making a big issue out of some of the things that or maybe being taught or they claim is being taught in schools or the kinds of materials that are available in school libraries, Entin said.

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The culture war, version 2.0 – Inside Higher Ed

It was among the most heated culture clashes of the 1980s: Stanfords decision in 1988 to cashier its freshman Western Civilization requirement.

If youre my age, you vividly remember the battle cry of the proponents of change: Hey, hey, ho, ho, Western cultures got to go.

The required reading list, which consisted of 15 classic texts, was reduced to six. Dantes Inferno was replaced by I, Rigoberta Menchu: An Indian Woman in Guatemala. Thomas Aquinas and Thomas More were out; Zora Neale Hurstons Their Eyes Were Watching God was in. John Locke and John Stuart Mill were replaced by the UN Declaration of Human Rights and examples of Rastafarian poetry, while Virgil, Cicero and Tacitus gave way to Frantz Fanons The Wretched of the Earth, a veritable handbook of revolutionary practice and social reorganization (according to the books dust jacket).

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The Wall Street Journals editorial board was outraged by what it saw as Stanfords decision to compromise the universitys intellectual seriousness. A number of Stanford faculty members, including the Pulitzer Prizewinning historian of slavery, race and gender Carl Degler, also voiced opposition to the change. With words that havent aged well, the author of books like Neither Black Nor White: Slavery and Race Relations in Brazil and the United States and At Odds: Women and the Family in America From the Revolution to the Present insisted that Few historians believe that the culture of this country has been seriously influenced by ideas from Africa, China, Japan or indigenous North America.

I bring up this episode because it underscores the centrality of the humanities to the late 20th centurys culture wars. At stake, many academics and intellectuals believed, was, in the words of the intellectual historian Andrew Hartman, nothing less than a war over the nations soul.

Sure, the humanities were often wielded by neoconservative editorialists and politicians as a political cudgel to attack the multicultural left. But an essential fact remains: the humanities mattered in a way that they dont today. As Hartman puts it in the second edition of his history of the culture wars of the 1970s, 80s and 90s:

A debate about whether Locke or Fanon deserves a place in a national curriculuma debate about what should constitute common knowledgecould only happen between people who share an understanding that education is a social good.

We are talking about a moment in time when a University of Chicago classicist and philosopher could write an anti-utilitarian defense of the humanities that treated learning as an erotic act and sell an astonishing 400,000 copies of the book in its first year and double that number in its second. Allan Bloom regarded a humanities education as:

A space between the intellectual wasteland [an undergraduate] has left behind and the inevitable dreary professional training that awaits him after the baccalaureate.

The kulturkmpf of the 1970s, 80s and 90s foregrounded the humanities as they had never been foregrounded before. Perhaps you recall some of the major controversies of that era:

Sure, the humanities were often wielded by editorialists, intellectuals and policy makers as a political cudgel. That said, the humanities mattered in a way they dont today. Better to be the subject of bitter political debate than to be marginalized or dismissed as irrelevant. In Hartmans words:

The left won those culture wars. But the victories have proven Pyrrhic. These days, not enough students want to study the humanities and justify their existence to cost-conscious administrators and few public voices are heard defending them, especially conservative voices.

Superficially, todays cultural conflictsover The New York Timess 1619 Project or critical race theory or intersectionality or postmodernism or gender ideology or decolonizationresemble those of three, four or five decades ago. Yet something profound has changed. As Hartman explains, some of the older struggles subsided due to the progressive lefts success in taking over major cultural institutionsart museums and foundations, as well as many academic humanities programs and professional societies. At the same time, economic anxiety and class resentment have mapped onto cultural divisions to make the culture wars angrier [and] more tribal.

Then theres the growing prevalence of political theater. Thanks, in part, to social media and the internet, public debates today favor the sensational over the substantive, the superficial over the serious and the visceral over the thoughtful. Hyperbole, overstatement, deliberate provocation are the order of the day. The academy has, I fear, fanned the flames, with activist scholars blurring the line between political action and scholarly claims, further debasing public discourse.

The temptation to speak out, even among those with no special expertise or insight, is apparently unstoppable. Artists, authors, intellectuals, professors and scholarly associations are signing open letters. Their purpose is a bit unclear, apart from simply saying something, showing their allegiance, signaling their virtue and engaging in a bit of self-promotion and networking.

With acid words, Nina Power, the English philosopher, writes, For someone working in the culture industries, the only thing worse than having the wrong position on a political controversy is having no position at all. These figures feel impelled to pronounce on anything and everything, staking a political stand on matters ranging from microaggressions to macropolitics. She is struck by the seeming hypocrisy of those who in the past de-platformed, ostracized and deprived of income, that is, canceled, others, who now speak out against what they regard as a new McCarthyism.

What happened?

James Davison Hunter, a professor of religion, culture and social theory at the University of Virginia, offered an explanation in an important if now largely forgotten 2017 Washington Post essay. In this piece, the author of a classic 1991 study, Culture Wars, traces how the earlier conflicta battle over sexuality, religion, family and the humanitiesmorphed and metastasized into a class war over globalization, immigration and the changing boundaries of legitimate pluralism, pitting the college-educated professional class against the non-college-educated lower middle and working classes.

For many middle- and low-wage workers, stagnating wages, declining union membership, lost manufacturing jobs and soaring income inequality undercut their hopes for a better life. Even worse, these groups saw their values and beliefs ridiculed as bigoted, homophobic, misogynist, xenophobic and backward by a relatively privileged and powerful elite.

Hunter cited a UVA survey that reported that seven of 10 of the less educated believe that the most educated and successful people in America are more interested in serving themselves than in serving the common good. Cynicism, mistrust and a sense of powerlessness were much higher among those with lower levels of schooling:

The poorly educated are one and a half times more likely than the college educated to hold the highest levels of distrust of the government; nearly three times more likely to be highly cynical of politicians; and over twice as likely to express the highest levels of alienation from the political process. Among the poorly educated who are religiously conservative, the levels of distrust, cynicism and alienation are even higher.

The cultural and class divide has had profound consequences for the humanities.

Today, the humanities increasingly exist on the cultures margins, with humanities faculty largely dismissed as politically predictable, their professional societies regarded as hyperpoliticized, their scholarship treated as irrelevant at best and partisan claptrap at worst.

Not surprisingly, humanists voices grow ever louder as their impact and influence grows progressively weaker.

To be sure, the most vocal attacks on the humanities are found in red states like Florida. But the real threats to the humanitiesthe continued decline in majors, the downsizing and even closure of departments, the increasing reliance on adjuncts, falling sales of academic books in humanities disciplines, flagging attendance at professional meetings, and shifting gen ed courses into high schoolis occurring apace in the blue states, too. Equally worrisome is the fact that the programs that do attract a growing number of undergraduates, including those in ethnic studies and gender and sexuality, increasingly think of themselves as part of the social sciences, not the humanities.

In a recent essay on the humanities future, the Times opinion columnist Ross Douthat makes a powerful case that in an era of scarcer resources, declining birth rates, sustained political conflict and students seeking a marketable credential, the humanities need Republican friends.

Instead, he avers, the humanities are doing a lot to alienate potential supporters. He quotes at length Tyler Austin Harper, an environmental studies professor at Bates College and a man of the left:

How did anyone think we could get away with being nakedly ideological for years without any chickens coming home to roost? Universities have always been tacitly left-leaning and faculty have always been openly so, but institutions have never been this transparently, officially political. Almost every single job ad in my field/related fields this year has some kind of brazenly politicized language.

Our society desperately needs the humanities and a functional public higher education system more broadly. And at the very moment were under sustained assault, some of us are still pouring fuel on Chris Rufos bonfire.

Douthat makes it clear that humanities programs cant build support among those who want to demote higher ed into a high-class trade school offering vocational training and building human capital, no matter how much we speak about imparting transferable skills or instilling critical thinking abilities or cross-cultural competencies.

But there are other conservatives who do respect the traditional value of a humanities education: cultural literacy, aesthetic appreciation, civic-mindedness, ethical thinking and historical perspective. Shouldnt we do more to appeal to those people, too?

What these folks wantand what I also desireis a greater emphasis on rigor, analysis, writing and communicating. Dont worry: imparting those skills wont make the humanities disciplines instrumental. Especially in the age of generative AI, when coding might be replaced by Alexa-like human commands, its hard for anyone in any political party to say, well, we dont need creative thinkers anymore or problem solvers, just coders/engineers.

Sure, students can read literature or history or popular philosophy books and visit museums on their own. But much of what I most enjoyed about my humanities classes was responding to the same work together, discussing it and having others to bounce ideas off. Or, in the case of experiencing an opera or film or other artistic work, bearing witness to something magical together.

The real failure of those of us who teach in the humanities today is not partisanship or politicization or an embrace of postmodern relativism. Its that as a result of hyperspecialization, prioritization of research over teaching and mentoring, and the production of scholarship inaccessible to a broader public, weve lost sight of the humanities true purpose.

That purpose is to understand the human experience in its complexity across time and place, to cultivate empathy and ethical insight, nurture aesthetic sensibilities, preserve collective memory and achievements, encourage social critique, inspire creativity and debate enduring questions about beauty, divinity, evil, human nature, justice and morality.

Disagree with this understanding of the humanities purpose if you wish. Treat the humanities as a pathway to advocacy and social justice if you will. But if you do that , dont be surprised to find our fields pushed even more into the cultures margins.

Youll be free to pontificate as you wish, but no one will be listening.

Steven Mintz is professor of history at the University of Texas at Austin.

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The culture war, version 2.0 - Inside Higher Ed

Musk and AI: Less culture wars, more Star Wars – POLITICO

With help from Derek Robertson

Elon Musk. | Alain Jocard/AFP via Getty Images

This weekend, Elon Musk unveiled the beta version of Grok, his new AI chatbot, which drew deeply on science fiction references: the bots name refers to the Martian science fiction novel Stranger in a Strange Land.

Musks early pitches for the project emphasized how politically different it would be from existing chatbots like ChatGPT. He unveiled it in an April interview with conservative pundit Tucker Carlson in which he described his interest in AI as motivated by fears that existing models, like the ones created by OpenAI, were baking in lefty bias. Im worried about the fact that its being trained to be politically correct, he said.

But his latest framing offers a vision of the future that is more, well, future-y. Per this weekends announcement, Grok has been released to a small number of users for beta testing, with plans to roll it out to premium subscribers of X, formerly known as Twitter.

In unveiling the bot on Saturday, Musks firm, xAI, cited a very different kind of inspiration: Grok, the announcement began, is an AI modeled after the Hitchhikers Guide to the Galaxy.

Tech industry watchers say there is a good reason for this evolution. While stoking culture war controversy can help generate buzz, many are skeptical outrage can attract a large number of users.

Sarcastic replies will entertain Musk superfans, but theyll ultimately be measured by their accuracy, said Nu Wexler, a former Senate staffer who has worked at Facebook and Twitter. Like social media platforms and search engines, theres not a big market for anti-woke AI, or any chatbots with a distinct political bent.

Musks brand has long been wrapped up in the futuristic technologies produced by his companies, which he has tied to long-term goals for the future, like colonizing the solar system.

In recent years, though, his public persona has become more political. Hes become an outspoken critic of progressive mores, describing his acquisition of Twitter since rebranded as X last year as part of a quest to defeat the woke mind virus. Musk has tied his anti-woke quest to his hands-off approach to moderation, an approach that has also allowed him to cut costs and led to a European Commission investigation of Xs compliance with the continents digital content rules.

With Grok, Musk appears to have taken a new tack. He has pledged Grok will be based (the antonym of woke in online slang), but hes leading his pitch with the vaguer offer that Grok will be spicy.

The bot is not yet widely available for testing, but so far spicy seems to be more PG-13 than politically explosive.

Asked for help making cocaine, in one exchange highlighted by Musk, Grok offered vague instructions like obtain a chemistry degree before adding Just kidding and adding a disclaimer that disavows illegal activity. Another Grok answer that Musk tweeted compared a computer programming challenge to trying to keep up with a never-ending orgy.

Oh this is gonna be fun Musk remarked.

What about the technicals? One of the big selling points touted this weekend was the capability to use data from X to provide up-to-date responses. OpenAIs ChatGPT does not incorporate information about events that have occurred in recent months. GPT-4 cited an April 2023 cutoff when explaining that it could not respond to DFDs request to discuss the recent news about Grok.

But that would not exactly revolutionize the current state of AI. Microsoft Bings Copilot, for one, already offers responses that incorporate information about recent events. Asked by DFD Monday morning about the release, Copilot responded, Grok is being trained by having real-time access to information from the platform, meaning X, before going on to cite more details of the rival chatbots release.

So for the moment, Musks promise for the future of AI is leaning heavily into zaniness and cinematic allusion. Hes also invoked Terminator and 2001: A Space Odyssey in discussing his AI ambitions. What if they just one day get a software update and theyre not so friendly anymore? Musk mused in a conversation with British Prime Minister Rishi Sunak on Thursday, Then weve got a [Terminator director] James Cameron movie on our hands.

Given Musks sweeping ambitions for his AI, its probably not a bad thing that hes mining sci-fi for scenarios to avoid: For one thing, he tweeted this weekend that hed like to one day integrate Grok into his Tesla vehicles.

A message from CTIA The Wireless Association:

CTIA Wireless Foundation is at the forefront of social innovation powered by wireless. Its signature initiative, Catalyst, is a grant program accelerating mobile-first solutions to pressing challenges in American communities. The Catalyst 2023 Winners are using 5G to address cyberbullying, education inequities and veterans mental health. Learn more.

As AI policy fights take over Washington, K Street is cashing in.

POLITICOs Hailey Fuchs and Brendan Bordelon reported over the weekend on how the growing field of AI policy has all the makings of a big payday for the lobbying industry think the crypto lobbying blitz, but bigger.

Hailey and Brendan write that AI lobbyists say nearly every industry has realized it will have to reckon with AI, with groups from Nike to the Mayo Clinic looking for an information advantage. But theres just one problem, at least for now: institutional Washington isnt exactly crawling with AI experts.

Every lobbying firm in town is trying to make themselves out to be an expert in everything to try and lure in clients, so AI is just one of them, one lobbyist said. Id be hard-pressed to name you an AI expert downtown. Its hard enough to pick the AI experts in policymaking positions. Derek Robertson

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Now that last weeks AI Safety Summit is over, whats going to actually happen?

POLITICOs Morning Tech U.K. newsletter recapped some of the actionables this morning, from international research collaborations to the important topics that didnt get covered during the summit. A few of their takeaways:

Setting up a research network. The Bletchley Declaration called for a research group meant to complement all involved countries AI safety programs. A difficult enough task in its own right, this group also notably includes China, with whom there are plenty of barriers to that level of cooperation already.

Pulling together a report. And that research partnership also calls for a state of the science report on frontier model capabilities and risks. Mariano-Florentino Cullar, president of Carnegie Endowment for International Peace and one of the key advocates for this push, called for reports at a pace of every one to six months.

Oh yeah, and killer robots. The military use of AI went strangely undiscussed at a summit ostensibly all about safety. Also last week, the United States made a declaration on responsible military use of AI that 31 countries have already endorsed.

Stay in touch with the whole team: Ben Schreckinger ([emailprotected]); Derek Robertson ([emailprotected]); Mohar Chatterjee ([emailprotected]); Steve Heuser ([emailprotected]); Nate Robson ([emailprotected]) and Daniella Cheslow ([emailprotected]).

If youve had this newsletter forwarded to you, you can sign up and read our mission statement at the links provided.

A message from CTIA The Wireless Association:

Innovative social entrepreneurs are taking advantage of the power of wireless and 5Gs speed, efficiency, and versatility to create groundbreaking solutions. CTIA Wireless Foundations Catalyst program awards over $200,000 each year to social entrepreneurs using wireless for good. The Catalyst 2023 Winners ReThink, Dope Nerds and Healium are using 5G to combat online harassment, provide STEM education to underserved students and deliver veteran mental health services. CTIA Wireless Foundation is committed to supporting social entrepreneurs that may face barriers to accessing capital, and the Catalyst 2023 winners have lived experiences with the issues they are working to solve, giving them the perspective and passion needed to make a difference. CTIA Wireless Foundation is proud to support the trailblazing, mobile-first work of the 2023 Catalyst Winners. Learn more.

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Grow Your Machine Learning Capabilities With Bitgrit Competitions – The Crypto Basic

Data is the driver of decision-making and innovation in todays world, and the race to harness its potential is a journey of continual learning and collaboration. This is the cornerstone of machine learning, a field that thrives on the ability to interpret complex data and convert it into actionable insights. The aspiration to excel in this domain often leads enthusiasts to a crossroad: a quest to find a way to not only challenge their skills but also nurture them. This is where bitgrit steps in, offering a confluence of competition, learning, earning, and real-world problem-solving.

Bitgrit is a competitive space, community, and marketplace for data scientists and AI enthusiasts to demonstrate, hone, and monetize their skills through various competitions. These competitions are a gateway to a world where real-world problems posed by companies become challenges awaiting solutions from a global community of data scientists.

With each competition, bitgrit aims to accelerate the journey of discovery and solution creation, advancing machine learning through challenges.

Bitgrits ecosystem is a meticulously crafted space fostering innovation, community engagement, and real-world problem-solving. It seamlessly intertwines blockchain technology and AI, creating an environment where data scientists can interact, learn, and contribute, while businesses access a reservoir of AI expertise. Utilizing blockchains distributed ledger technology (DLT), bitgrit records user contributions to competitions and projects, ensuring fair revenue share upon completion, which underpins the platforms commitment to transparency and fair compensation.

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With the vision of democratizing AI and a mission to evolve into a global platform congregating data scientists for societal and business betterment, bitgrit is a thriving community where daily engagements lead to earning, learning, sharing, and growth.

At the core of this ecosystem is the BGR token, streamlining various interactions within the community. Whether its earning tokens through competition engagement, transacting in the AI Marketplace, or accessing the job board, the BGR token is a catalyst in fostering a vibrant and engaging community.

The bitgrit ecosystem, a harmonious blend of competitions, a job board, an AI Marketplace, and community-driven forums, offers data scientists a platform to either kickstart or propel their careers forward. It stands as a bridge between real-world business challenges and innovative AI solutions, driving the field of AI and machine learning forward with a community of passionate data scientists.

With future integrations like discussion forums, user wallet integration, and a refined API for blockchain-based data transactions, bitgrit is poised not just as a hub for AI and machine learning, but a cornerstone for collaborative innovation in the data science realm.

The bitgrit community is more than just a gathering of data enthusiasts. With a strong community of more than 30,000 engineers worldwide, its a rich reservoir of talent and innovative AI and ML solutions that businesses can tap into. The platforms dual nature, as both a competition arena and a recruiting hub, has proven to be a potent tool for companies seeking to solve complex problems or acquire top-tier talent.

Several notable enterprises have successfully utilized the bitgrit platform to advance their machine learning initiatives. Companies like SoftBank, Atrae, CTRL-F, and even governmental bodies like NIH/NASA have engaged the bitgrit community to solve complex challenges. The collaborative competitions on bitgrit not only provided needed solutions but also offered a window into the pool of talent available for recruitment.

For instance, one of the competitions hosted on bitgrit was the NASA Tournament Lab competition, a collaborative endeavor co-orchestrated with NCATS (The National Center for Advancing Translational Sciences) and NLM (National Library of Medicine). This competition showcased bitgrits potential as a conduit linking scientific institutions with a global community of data scientists. Through this engagement, the combined intellect of the community was harnessed to develop solutions that accelerated scientific research in medicine, particularly leveraging the capabilities of natural language processing.

Furthermore, the success stories extend to the individual level as well. Competition winners not only clinch financial rewards but also catch the eye of potential employers. The platform serves as a launchpad, propelling winners into the radar of companies keen on harnessing fresh, innovative minds to further their projects. Some of these companies have gone the extra mile to interview winners, seeking deeper insights into the problems tackled during the competitions, and exploring possibilities of future collaborations.

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Join the bitgrit community and participate in the live bitgrit AI-Generated Text Identification Challenge. Discover the different opportunities awaiting you in the realm of machine learning and data science.

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Disclaimer: This content is informational and should not be considered financial advice. The views expressed in this article may include the author's personal opinions and do not reflect The Crypto Basics opinion. Readers are encouraged to do thorough research before making any investment decisions. The Crypto Basic is not responsible for any financial losses.

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Constrained DFT-based magnetic machine-learning potentials for magnetic alloys: a case study of FeAl | Scientific … – Nature.com

Magnetic multi-component moment tensor potential (mMTP)

The concept of magnetic multi-component Moment Tensor Potential (mMTP) presented in the current research is based on the previously developed non-magnetic MTP for multi-component systems41,42 and magnetic MTP for single-component systems35.

The mMTP potential is local, i.e., the energy of the atomistic system is a sum of energies of individual atoms:

$$begin{aligned} E = sum _{i=1}^{N_a}E_i, end{aligned}$$

(1)

where i stands for the individual atoms in an (N_a)-atom system. We note that any configuration includes lattice vectors ({{varvec{L}}} = {{{varvec{l}}}_1,{{varvec{l}}}_2,{{varvec{l}}}_3}), atomic positions ({{varvec{R}}} = {{{varvec{r}}}_1, ldots , {{varvec{r}}}_{N_a}}), types (Z = {z_1,ldots ,z_{N_{a}}}) (we also denote (N_{rm types}) by the total number of atomic types in the system), and magnetic moments (M = {m_1,ldots ,m_{N_a}}). The energy of the atom (E_i), in turn, has the form:

$$begin{aligned} E_i = sum _{alpha =1}^{alpha _{rm max}} xi _{alpha }B_{alpha }({mathfrak n}_i), end{aligned}$$

(2)

where ({{varvec{xi }}} = {xi _{alpha } }) are the linear parameters to be optimized and (B_alpha) are the so-called basis functions, which are contractions of the descriptors25 of atomistic environment ({mathfrak n}_i), yielding a scalar. The (alpha _text {max}) parameter can be changed to provide potentials with different amount of parameters35.

The descriptors are composed of the radial part, i.e., the scalar function depending on the interatomic distances and atomic magnetic moments, and the angular part, which is a tensor of rank (nu):

$$begin{aligned} M_{mu ,nu }({mathfrak n}_i)=sum _{j} f_{mu }(| {{varvec{r}}}_{ij}|,z_i,z_j,m_i,m_j)underbrace{{{varvec{r}}}_{ij}otimes ...otimes {{varvec{r}}}_{ij}}_nu text { times }, end{aligned}$$

(3)

where ({mathfrak n}_i) stands for the atomic environment, including all the atoms within the (R_text {cut}) distance (or less) from the central atom i, (mu) is the number of the radial function, (nu) is the rank of the angular part tensor, (|{{varvec{r}}}_{ij}|) is the distance between the atoms i and j, (z_i) and (z_j) are the atomic types, (m_i) and (m_j) are the magnetic moments of the atoms.

The radial functions are expanded in a basis of Chebyshev polynomials:

$$begin{aligned} f_{mu }(|r_{ij}|,z_i,z_j,m_i,m_j) = sum _{zeta =1}^{N_{phi }} sum _{beta =1}^{N_{psi }}sum _{gamma =1}^{N_{psi }}c_{mu ,z_i,z_j}^{zeta ,beta ,gamma } phi _{zeta }(|{varvec{r}}_{ij}|) psi _{beta }(m_i)psi _{gamma }(m_j) (R_{rm cut} - |{varvec{r}}_{ij}|)^2. end{aligned}$$

(4)

Here ({{varvec{c}}} = {c_{mu ,z_i,z_j}^{zeta ,beta ,gamma }}) are the radial parameters to be optimized, each of the functions (phi _{zeta }(|{varvec{r}}_{ij}|)), (psi _{beta }(m_i)), (psi _{gamma }(m_i)) is a Chebyshev polynomial of order (zeta), (beta) and (gamma) correspondingly, taking values from (-1) to 1. The function (phi _{zeta }(|{varvec{r}}_{ij}|)) yields the dependency on the distance between the atoms i and j, while the functions (psi _{beta }(m_i)) and (psi _{gamma }(m_j)) yield the dependency on the magnetic moments of the atoms i and j, correspondingly. The arguments of the functions (phi _{zeta }(|{varvec{r}}_{ij}|)) are on the interval ((R_{rm min},R_{rm cut})), where (R_{rm min}) and (R_{rm cut}) are the minimum and maximum distance, correspondingly, between the interacting atoms. The functions (psi _{beta }(m_i)) and (psi _{gamma }(m_j)) are of the same structure, which we explain for the case of the former one. The argument of the function (psi _{beta }(m_i)) is the magnetic moment of the atom i, taking the values on the ((-M_{rm max}^{z_i},M_{rm max}^{z_i})) interval. The value (M_{rm max}^{z_i}) itself depends on the type of atom (z_i), and is determined as the maximal absolute value of the magnetic moment for atom type (z_i) in the training set. Similar to the conventional MTP, the term ((R_{rm cut} - |{varvec{r}}_{ij}|)^2) provides smooth fading to 0 when approaching the (R_{rm cut}) distance, in accordance with the locality principle (1).

We note that magnetic degrees of freedom (m_i) from (4) are collinear, i.e., they can take negative or positive values as projection onto the Z axis (though the choice of the axis is arbitrary). This way, in comparison to non-magnetic atomistic systems with N atoms, in which the amount of degrees of freedom equals 4N (namely 3N for coordinates and N for types), for the description of magnetic systems additional N degrees of freedom are introduced, standing for the magnetic moment (m_i) of each atom. The amount of parameters entering the radial functions (Eq. 4) also increases in mMTP compared to the conventional MTP41,42. Namely, in MTP this number equals (N_{mu } cdot N_{phi } cdot N_{rm types}^2), while in mMTP it is (N_{mu } cdot N_{phi } cdot N_{rm types}^2 cdot N_{psi }^2). Thus, if we take (N_{psi } = 2) (which is used in the current research), the amount of the parameters entering the radial functions would be four times more in mMTP then in MTP.

We denote all the mMTP parameters by ({varvec{theta }}= {{varvec{xi }}, {varvec{c}} }) and the total energy (1) of the atomic system by (E=E({{varvec{theta }}})=E({{varvec{theta }}};M)=E({{varvec{theta }}};{{varvec{L}}},{{varvec{R}}},Z,M)).

The tensor (Eq. (4)) includes collinear magnetic moments in its functional form. However, it is not invariant with respect to the inversion of magnetic moments, i.e., (E({{varvec{theta }}};M) ne E({{varvec{theta }}};-M)), while both original and spin-inverted configurations should yield the same energy due to the arbitrary orientation of the projection axis, which we further call the magnetic symmetry.

We use data augmentation followed by explicit symmetrization with respect to magnetic moments to train a symmetric mMTP as we discuss below. Assume we have K configurations in the training set with DFT energies (E_k^{rm DFT}), forces ({varvec{f}}^{rm DFT}_{i,k}), and stresses (sigma ^{rm DFT}_{ab,k}) ((a,b=1,2,3)) calculated. We find the optimal parameters (bar{{{varvec{theta }}}}) (fit mMTP) by minimizing the objective function:

$$begin{aligned} &sum _{k=1}^{K} Biggl [ w_{rm e} Biggl | frac{E_k ({varvec{theta }}; M) + E_{k}({varvec{theta }}; -M)}{2} - E_{k}^{rm DFT}Biggr |^2 \&quad + w_{rm f} sum _{i=1}^{N_a} Biggl | frac{{varvec{f}}_{i,k}({varvec{theta }};M) + {varvec{f}}_{i,k}({varvec{theta }};-M)}{2} - {varvec{f}}^{rm DFT}_{i,k}Biggr |^2 \&quad +w_{rm s} sum _{a,b=1}^{3} Biggl | frac{sigma _{ab,k}({varvec{theta }};M)+sigma _{ab,k}({varvec{theta }};-M)}{2} -sigma ^{rm DFT}_{ab,k}Biggr |^2 Biggr ], end{aligned}$$

(5)

where (w_{rm e}), (w_{rm f}), and (w_{rm s}) are non-negative weights. By minimizing (5) we find such optimal parameters (bar{{{varvec{theta }}}}) that yield (E_k (bar{{varvec{theta }}}; M) approx E_k (bar{{varvec{theta }}}; -M)), (k = 1, ldots , K) (the same fact takes place for the mMTP forces and stresses), i.e., we symmetrize the training set to make mMTP learn the required symmetry from the data itselfthis is called data augmentation.

Next, we modify mMTP to make the energy used for the simulations (e.g., relaxation of configurations) to satisfy the exact symmetry:

$$begin{aligned} E^{rm symm}(bar{{{varvec{theta }}}};M) = dfrac{E(bar{{varvec{theta }}};M)+E(bar{{varvec{theta }}};-M)}{2}. end{aligned}$$

(6)

That is, we substitute the mMTP energy (1) into (6) and get a functional form which satisfies the exact identity (E^{rm symm}(bar{{{varvec{theta }}}};M) = E^{rm symm}(bar{{{varvec{theta }}}};-M)) for any configuration. We also note that (E (bar{{varvec{theta }}}) approx E^{rm symm}(bar{{{varvec{theta }}}})).

We use the cDFT approach with hard constraints(i.e., Lagrange multiplier) as proposed by Gonze et al. in Ref.19. One way to formulate it is to first note that in a single-point DFT calculation we minimize the Kohn-Sham total energy functional (E[rho ; {{varvec{R}}}]) with respect to the electronic density (rho =rho (r)) (here (rho) combines the spin-up and spin-down electron densities), keeping the nuclei position ({{varvec{R}}}) fixed. In other words, we solve the following minimization problem:

$$begin{aligned} E_{rm DFT}({{varvec{R}}}) = min _rho E[rho ; {{varvec{R}}}], end{aligned}$$

and from the optimal (rho ^* = mathrm{arg,min} E[rho ; {{varvec{R}}}]) we can, e.g., find magnetization (m(r) = rho ^*_+ - rho ^*_-), where the subscripts denote the spin-up ((+)) and spin-down () densities. The magnetic moment of the ith atom can be found by integrating m(r) over some (depending on the partitioning scheme) region around the atom:

$$begin{aligned} m_i = int _{Omega _i} m(r) textrm{d}r. end{aligned}$$

(7)

Since the minimizer (rho ^*) depends on ({{varvec{R}}}), (m_i) are also the functions of ({{varvec{R}}}).

According to the cDFT approach19, we now formulate the problem of minimizing (E[rho ; {{varvec{R}}}]) in which not only ({{varvec{R}}}),but also (rho) is allowed to change only subject to constraints (7):

$$begin{aligned} begin{array}{rcl} E_{rm cDFT}(rho, {{varvec{R}}}, M) =&{} min _rho &{} E[rho ; {{varvec{R}}}] \ &{} text {subject to} &{} m_i = int _{Omega _i} big (rho _{+}(r)-rho _-(r)big ) textrm{d}r. end{array} end{aligned}$$

The algorithmic details of how this minimization problem is solved, and how the energy derivatives (forces, stresses, torques) are computed, are described in detail in Ref.19.

We used the ABINIT code43,44 for DFT (and cDFT recently developed and described in Ref.19) calculations with (6times 6times 6) k-point mesh and cutoff energy of 25 Hartree (about 680 eV). We utilized the PAW PBE method with the generalized gradient approximation. We applied constraints on magnetic moments of all atoms during cDFT calculations.

We fitted an ensemble of five mMTPs with 415 parameters in order to quantify the uncertainty of mMTPs predictions. For each mMTP we took (R_{rm min} = 2.1 ~) , (R_{rm cut} = 4.5 ~), (M_{rm max}^{rm Al} = 0.1 ~mu _B), and (M_{rm max}^{rm Fe} = 3.0 ~mu _B). The weights in the objective function (5) were (w_{rm e} = 1), (w_{rm f} = 0.01) (^2), and (w_{rm s} = 0.001).

See the article here:
Constrained DFT-based magnetic machine-learning potentials for magnetic alloys: a case study of FeAl | Scientific ... - Nature.com