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Tianji Cai, Garrett W. Merz, François Charton, Niklas Nolte, Matthias Wilhelm, Kyle Cranmer, Lance J. Dixon

We pursue the use of deep learning methods to improve state-of-the-art computations in theoretical high-energy physics. Planar N = 4 Super Yang-Mills theory is a close cousin to the theory that describes Higgs boson production at the Large Hadron Collider; its scattering amplitudes are large mathematical expressions containing integer coefficients. In this paper, we apply Transformers to predict these coefficients. The problem can be formulated in a language-like representation amenable to standard cross-entropy training objectives. We design two related experiments and show that the model achieves high accuracy (> 98%) on both tasks. Our work shows that Transformers can be applied successfully to problems in theoretical physics that require exact solutions.

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Abhijith Gandrakota, Lily Zhang, Aahlad Puli, Kyle Cranmer, Jennifer Ngadiuba, Rajesh Ranganath, Nhan Tran

Anomaly, or out-of-distribution, detection is a promising tool for aiding discoveries of new particles or processes in particle physics. In this work, we identify and address two overlooked opportunities to improve anomaly detection for high-energy physics. First, rather than train a generative model on the single most dominant background process, we build detection algorithms using representation learning from multiple background types, thus taking advantage of more information to improve estimation of what is relevant for detection. Second, we generalize decorrelation to the multi-background setting, thus directly enforcing a more complete definition of robustness for anomaly detection. We demonstrate the benefit of the proposed robust multi-background anomaly detection algorithms on a high-dimensional dataset of particle decays at the Large Hadron Collider.

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Kyle Cranmer, Gurtej Kanwar, Sébastien Racanière, Danilo J. Rezende, Phiala E. Shanahan

Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising tool in this space, building on the success of this approach in applications such as image, text, and audio generation. Often, however, generative tasks in scientific domains have unique structures and features -- such as complex symmetries and the requirement of exactness guarantees -- that present both challenges and opportunities for ML. This Perspective outlines the advances in ML-based sampling motivated by lattice quantum field theory, in particular for the theory of quantum chromodynamics. Enabling calculations of the structure and interactions of matter from our most fundamental understanding of particle physics, lattice quantum chromodynamics is one of the main consumers of open-science supercomputing worldwide. The design of ML algorithms for this application faces profound challenges, including the necessity of scaling custom ML architectures to the largest supercomputers, but also promises immense benefits, and is spurring a wave of development in ML-based sampling more broadly. In lattice field theory, if this approach can realize its early promise it will be a transformative step towards first-principles physics calculations in particle, nuclear and condensed matter physics that are intractable with traditional approaches.

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Ryan Abbott, Michael S. Albergo, Aleksandar Botev, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Gurtej Kanwar, Alexander G. D. G. Matthews, Sébastien Racanière, Ali Razavi, Danilo J. Rezende, Fernando Romero-López, Phiala E. Shanahan, Julian M. Urban

Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow architectures facilitating the generalization to higher-dimensional lattice geometries. Specifically, we discuss masked autoregressive transformations with tractable and unbiased Jacobian determinants, a key ingredient for scalable and asymptotically exact flow-based sampling algorithms. For concreteness, results from a proof-of-principle application to SU(3) lattice gauge theory in four space-time dimensions are reported.

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Francesco Armando Di Bello, Anton Charkin-Gorbulin, Kyle Cranmer, Etienne Dreyer, Sanmay Ganguly, Eilam Gross, Lukas Heinrich, Lorenzo Santi, Marumi Kado, Nilotpal Kakati, Patrick Rieck, Matteo Tusoni

A configurable calorimeter simulation for AI (COCOA) applications is presented, based on the Geant4 toolkit and interfaced with the Pythia event generator. This open-source project is aimed to support the development of machine learning algorithms in high energy physics that rely on realistic particle shower descriptions, such as reconstruction, fast simulation, and low-level analysis. Specifications such as the granularity and material of its nearly hermetic geometry are user-configurable. The tool is supplemented with simple event processing including topological clustering, jet algorithms, and a nearest-neighbors graph construction. Formatting is also provided to visualise events using the Phoenix event display software.

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Philipp Berens, Kyle Cranmer, Neil D. Lawrence, Ulrike von Luxburg, Jessica Montgomery

This report documents the programme and the outcomes of Dagstuhl Seminar 22382 "Machine Learning for Science: Bridging Data-Driven and Mechanistic Modelling". Today's scientific challenges are characterised by complexity. Interconnected natural, technological, and human systems are influenced by forces acting across time- and spatial-scales, resulting in complex interactions and emergent behaviours. Understanding these phenomena -- and leveraging scientific advances to deliver innovative solutions to improve society's health, wealth, and well-being -- requires new ways of analysing complex systems. The transformative potential of AI stems from its widespread applicability across disciplines, and will only be achieved through integration across research domains. AI for science is a rendezvous point. It brings together expertise from $\mathrm{AI}$ and application domains; combines modelling knowledge with engineering know-how; and relies on collaboration across disciplines and between humans and machines. Alongside technical advances, the next wave of progress in the field will come from building a community of machine learning researchers, domain experts, citizen scientists, and engineers working together to design and deploy effective AI tools. This report summarises the discussions from the seminar and provides a roadmap to suggest how different communities can collaborate to deliver a new wave of progress in AI and its application for scientific discovery.

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Ryan Abbott, Michael S. Albergo, Aleksandar Botev, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Alexander G. D. G. Matthews, Sébastien Racanière, Ali Razavi, Danilo J. Rezende, Fernando Romero-López, Phiala E. Shanahan, Julian M. Urban

Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the scale of toy models, and it remains to be determined whether they can be applied to state-of-the-art lattice quantum chromodynamics calculations. Assessing the viability of sampling algorithms for lattice field theory at scale has traditionally been accomplished using simple cost scaling laws, but as we discuss in this work, their utility is limited for flow-based approaches. We conclude that flow-based approaches to sampling are better thought of as a broad family of algorithms with different scaling properties, and that scalability must be assessed experimentally.

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Ryan Abbott, Michael S. Albergo, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Gurtej Kanwar, Sébastien Racanière, Danilo J. Rezende, Fernando Romero-López, Phiala E. Shanahan, Betsy Tian, Julian M. Urban

This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as stochastic estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD. Methods by which flow-based sampling approaches can be improved via standard techniques such as even/odd preconditioning and the Hasenbusch factorization are also outlined. Numerical demonstrations in two-dimensional U(1) and SU(3) gauge theories with $N_f=2$ flavors of fermions are provided.

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Michael S. Albergo, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Gurtej Kanwar, Sébastien Racanière, Danilo J. Rezende, Fernando Romero-López, Phiala E. Shanahan, Julian M. Urban

Recent results suggest that flow-based algorithms may provide efficient sampling of field distributions for lattice field theory applications, such as studies of quantum chromodynamics and the Schwinger model. In this work, we provide a numerical demonstration of robust flow-based sampling in the Schwinger model at the critical value of the fermion mass. In contrast, at the same parameters, conventional methods fail to sample all parts of configuration space, leading to severely underestimated uncertainties.

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Alexander Lavin, Hector Zenil, Brooks Paige, David Krakauer, Justin Gottschlich, Tim Mattson, Anima Anandkumar, Sanjay Choudry, Kamil Rocki, Atılım Güneş Baydin, Carina Prunkl, Olexandr Isayev, Erik Peterson, Peter L. McMahon, Jakob Macke, Kyle Cranmer, Jiaxin Zhang, Haruko Wainwright, Adi Hanuka, Manuela Veloso, Samuel Assefa, Stephan Zheng, Avi Pfeffer

The original "Seven Motifs" set forth a roadmap of essential methods for the field of scientific computing, where a motif is an algorithmic method that captures a pattern of computation and data movement. We present the "Nine Motifs of Simulation Intelligence", a roadmap for the development and integration of the essential algorithms necessary for a merger of scientific computing, scientific simulation, and artificial intelligence. We call this merger simulation intelligence (SI), for short. We argue the motifs of simulation intelligence are interconnected and interdependent, much like the components within the layers of an operating system. Using this metaphor, we explore the nature of each layer of the simulation intelligence operating system stack (SI-stack) and the motifs therein: (1) Multi-physics and multi-scale modeling; (2) Surrogate modeling and emulation; (3) Simulation-based inference; (4) Causal modeling and inference; (5) Agent-based modeling; (6) Probabilistic programming; (7) Differentiable programming; (8) Open-ended optimization; (9) Machine programming. We believe coordinated efforts between motifs offers immense opportunity to accelerate scientific discovery, from solving inverse problems in synthetic biology and climate science, to directing nuclear energy experiments and predicting emergent behavior in socioeconomic settings. We elaborate on each layer of the SI-stack, detailing the state-of-art methods, presenting examples to highlight challenges and opportunities, and advocating for specific ways to advance the motifs and the synergies from their combinations. Advancing and integrating these technologies can enable a robust and efficient hypothesis-simulation-analysis type of scientific method, which we introduce with several use-cases for human-machine teaming and automated science.

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