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Applications/Physics

Zebang Shen, Zhenfu Wang

The McKean-Vlasov equation (MVE) describes the collective behavior of particles subject to drift, diffusion, and mean-field interaction. In physical systems, the interaction term can be singular, i.e. it diverges when two particles collide. Notable examples of such interactions include the Coulomb interaction, fundamental in plasma physics, and the Biot-Savart interaction, present in the vorticity formulation of the 2D Navier-Stokes equation (NSE) in fluid dynamics. Solving MVEs that involve singular interaction kernels presents a significant challenge, especially when aiming to provide rigorous theoretical guarantees. In this work, we propose a novel approach based on the concept of entropy dissipation in the underlying system. We derive a potential function that effectively controls the KL divergence between a hypothesis solution and the ground truth. Building upon this theoretical foundation, we introduce the Entropy-dissipation Informed Neural Network (EINN) framework for solving MVEs. In EINN, we utilize neural networks (NN) to approximate the underlying velocity field and minimize the proposed potential function. By leveraging the expressive power of NNs, our approach offers a promising avenue for tackling the complexities associated with singular interactions. To assess the empirical performance of our method, we compare EINN with SOTA NN-based MVE solvers. The results demonstrate the effectiveness of our approach in solving MVEs across various example problems.

Applications/Physics

Sheikh Md Shakeel Hassan, Arthur Feeney, Akash Dhruv, Jihoon Kim, Youngjoon Suh, Jaiyoung Ryu, Yoonjin Won, Aparna Chandramowlishwaran

In the field of phase change phenomena, the lack of accessible and diverse datasets suitable for machine learning (ML) training poses a significant challenge. Existing experimental datasets are often restricted, with limited availability and sparse ground truth, impeding our understanding of this complex multiphysics phenomena. To bridge this gap, we present the BubbleML dataset which leverages physics-driven simulations to provide accurate ground truth information for various boiling scenarios, encompassing nucleate pool boiling, flow boiling, and sub-cooled boiling. This extensive dataset covers a wide range of parameters, including varying gravity conditions, flow rates, sub-cooling levels, and wall superheat, comprising 79 simulations. BubbleML is validated against experimental observations and trends, establishing it as an invaluable resource for ML research. Furthermore, we showcase its potential to facilitate the exploration of diverse downstream tasks by introducing two benchmarks: (a) optical flow analysis to capture bubble dynamics, and (b) neural PDE solvers for learning temperature and flow dynamics. The BubbleML dataset and its benchmarks aim to catalyze progress in ML-driven research on multiphysics phase change phenomena, providing robust baselines for the development and comparison of state-of-the-art techniques and models.

Applications/Physics

Anudhyan Boral, Zhong Yi Wan, Leonardo Zepeda-Núñez, James Lottes, Qing Wang, Yi-Fan Chen, John Anderson, Fei Sha

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES models the LES flow by treating each full-order trajectory as a random realization of the underlying dynamics, as such, the effect of small-scales is marginalized to obtain the deterministic evolution of the LES state. However, ideal LES is analytically intractable. In our work, we use a latent neural SDE to model the evolution of the stochastic process and an encoder-decoder pair for transforming between the latent space and the desired ideal flow field. This stands in sharp contrast to other types of neural parameterization of closure models where each trajectory is treated as a deterministic realization of the dynamics. We show the effectiveness of our approach (niLES – neural ideal LES) on two challenging chaotic dynamical systems: Kolmogorov flow at a Reynolds number of 20,000 and flow past a cylinder at Reynolds number 500. Compared to competing methods, our method can handle non-uniform geometries using unstructured meshes seamlessly. In particular, niLES leads to trajectories with more accurate statistics and enhances stability, particularly for long-horizon rollouts. (Source codes and datasets will be made publicly available.)

Applications/Physics

Wai Tong Chung, Bassem Akoush, Pushan Sharma, Alex Tamkin, Ki Sung Jung, Jacqueline Chen, Jack Guo, Davy Brouzet, Mohsen Talei, Bruno Savard 等

Analysis of compressible turbulent flows is essential for applications related to propulsion, energy generation, and the environment. Here, we present BLASTNet 2.0, a 2.2 TB network-of-datasets containing 744 full-domain samples from 34 high-fidelity direct numerical simulations, which addresses the current limited availability of 3D high-fidelity reacting and non-reacting compressible turbulent flow simulation data. With this data, we benchmark a total of 49 variations of five deep learning approaches for 3D super-resolution - which can be applied for improving scientific imaging, simulations, turbulence models, as well as in computer vision applications. We perform neural scaling analysis on these models to examine the performance of different machine learning (ML) approaches, including two scientific ML techniques. We demonstrate that (i) predictive performance can scale with model size and cost, (ii) architecture matters significantly, especially for smaller models, and (iii) the benefits of physics-based losses can persist with increasing model size. The outcomes of this benchmark study are anticipated to offer insights that can aid the design of 3D super-resolution models, especially for turbulence models, while this data is expected to foster ML methods for a broad range of flow physics applications. This data is publicly available with download links and browsing tools consolidated at https://blastnet.github.io.

Applications/Physics

Shashank Subramanian, Peter Harrington, Kurt Keutzer, Wahid Bhimji, Dmitriy Morozov, Michael Mahoney, Amir Gholami

Pre-trained machine learning (ML) models have shown great performance for awide range of applications, in particular in natural language processing (NLP)and computer vision (CV). Here, we study how pre-training could be used forscientific machine learning (SciML) applications, specifically in the context oftransfer learning. We study the transfer behavior of these models as (i) the pretrainedmodel size is scaled, (ii) the downstream training dataset size is scaled,(iii) the physics parameters are systematically pushed out of distribution, and (iv)how a single model pre-trained on a mixture of different physics problems canbe adapted to various downstream applications. We find that—when fine-tunedappropriately—transfer learning can help reach desired accuracy levels with ordersof magnitude fewer downstream examples (across different tasks that can even beout-of-distribution) than training from scratch, with consistent behaviour across awide range of downstream examples. We also find that fine-tuning these modelsyields more performance gains as model size increases, compared to training fromscratch on new downstream tasks. These results hold for a broad range of PDElearning tasks. All in all, our results demonstrate the potential of the “pre-train andfine-tune” paradigm for SciML problems, demonstrating a path towards buildingSciML foundation models. Our code is available as open-source.

Applications/Physics

Jinxi Li, Ziyang Song, Bo Yang

In this paper, we aim to model 3D scene dynamics from multi-view videos. Unlike the majority of existing works which usually focus on the common task of novel view synthesis within the training time period, we propose to simultaneously learn the geometry, appearance, and physical velocity of 3D scenes only from video frames, such that multiple desirable applications can be supported, including future frame extrapolation, unsupervised 3D semantic scene decomposition, and dynamic motion transfer. Our method consists of three major components, 1) the keyframe dynamic radiance field, 2) the interframe velocity field, and 3) a joint keyframe and interframe optimization module which is the core of our framework to effectively train both networks. To validate our method, we further introduce two dynamic 3D datasets: 1) Dynamic Object dataset, and 2) Dynamic Indoor Scene dataset. We conduct extensive experiments on multiple datasets, demonstrating the superior performance of our method over all baselines, particularly in the critical tasks of future frame extrapolation and unsupervised 3D semantic scene decomposition.

Applications/Physics

Zhuo Chen, Laker Newhouse, Eddie Chen, Di Luo, Marin Soljacic

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D $J_1$-$J_2$ Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.

Applications/Physics

Artur Toshev, Gianluca Galletti, Fabian Fritz, Stefan Adami, Nikolaus Adams

Machine learning has been successfully applied to grid-based PDE modeling in various scientific applications. However, learned PDE solvers based on Lagrangian particle discretizations, which are the preferred approach to problems with free surfaces or complex physics, remain largely unexplored. We present LagrangeBench, the first benchmarking suite for Lagrangian particle problems, focusing on temporal coarse-graining. In particular, our contribution is: (a) seven new fluid mechanics datasets (four in 2D and three in 3D) generated with the Smoothed Particle Hydrodynamics (SPH) method including the Taylor-Green vortex, lid-driven cavity, reverse Poiseuille flow, and dam break, each of which includes different physics like solid wall interactions or free surface, (b) efficient JAX-based API with various recent training strategies and three neighbor search routines, and (c) JAX implementation of established Graph Neural Networks (GNNs) like GNS and SEGNN with baseline results. Finally, to measure the performance of learned surrogates we go beyond established position errors and introduce physical metrics like kinetic energy MSE and Sinkhorn distance for the particle distribution. Our codebase is available under the URL: [https://github.com/tumaer/lagrangebench](https://github.com/tumaer/lagrangebench).

Applications/Physics

Louis Serrano, Lise Le Boudec, Armand Kassaï Koupaï, Thomas X Wang, Yuan Yin, Jean-Noël Vittaut, Patrick Gallinari

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and inverse problems like geometric design. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

Applications/Physics

Su Zheng, Haoyu Yang, Binwu Zhu, Bei Yu, Martin Wong

Computational lithography provides algorithmic and mathematical support for resolution enhancement in optical lithography, which is the critical step in semiconductor manufacturing. The time-consuming lithography simulation and mask optimization processes limit the practical application of inverse lithography technology (ILT), a promising solution to the challenges of advanced-node lithography. Although various machine learning methods for ILT have shown promise for reducing the computational burden, this field is in lack of a dataset that can train the models thoroughly and evaluate the performance comprehensively. To boost the development of AI-driven computational lithography, we present the LithoBench dataset, a collection of circuit layout tiles for deep-learning-based lithography simulation and mask optimization. LithoBench consists of more than 120k tiles that are cropped from real circuit designs or synthesized according to the layout topologies of famous ILT testcases. The ground truths are generated by a famous lithography model in academia and an advanced ILT method. Based on the data, we provide a framework to design and evaluate deep neural networks (DNNs) with the data. The framework is used to benchmark state-of-the-art models on lithography simulation and mask optimization. We hope LithoBench can promote the research and development of computational lithography. LithoBench is available at https://anonymous.4open.science/r/lithobench-APPL.

Applications/Physics

Yuanqi Du, Yingheng Wang, Yining Huang, Jianan Canal Li, Yanqiao Zhu, Tian Xie, Chenru Duan, John Gregoire, Carla Gomes

We introduce M$^2$Hub, a toolkit for advancing machine learning in materials discovery. Machine learning has achieved remarkable progress in modeling molecular structures, especially biomolecules for drug discovery. However, the development of machine learning approaches for modeling materials structures lag behind, which is partly due to the lack of an integrated platform that enables access to diverse tasks for materials discovery. To bridge this gap, M$^2$Hub will enable easy access to materials discovery tasks, datasets, machine learning methods, evaluations, and benchmark results that cover the entire workflow. Specifically, the first release of M$^2$Hub focuses on three key stages in materials discovery: virtual screening, inverse design, and molecular simulation, including 9 datasets that covers 6 types of materials with 56 tasks across 8 types of material properties. We further provide 2 synthetic datasets for the purpose of generative tasks on materials. In addition to random data splits, we also provide 3 additional data partitions to reflect the real-world materials discovery scenarios. State-of-the-art machine learning methods (including those are suitable for materials structures but never compared in the literature) are benchmarked on representative tasks. Our codes and library are publicly available at \url{https://github.com/yuanqidu/M2Hub}.

Applications/Physics

Atul Kumar Sinha, Daniele Paliotta, Bálint Máté, John Raine, Tobias Golling, François Fleuret

Deep learning methods have gained popularity in high energy physics for fast modeling of particle showers in detectors. Detailed simulation frameworks such as the gold standard \textsc{Geant4} are computationally intensive, and current deep generative architectures work on discretized, lower resolution versions of the detailed simulation. The development of models that work at higher spatial resolutions is currently hindered by the complexity of the full simulation data, and by the lack of simpler, more interpretable benchmarks. Our contribution is \textsc{SUPA}, the SUrrogate PArticle propagation simulator, an algorithm and software package for generating data by simulating simplified particle propagation, scattering and shower development in matter. The generation is extremely fast and easy to use compared to \textsc{Geant4}, but still exhibits the key characteristics and challenges of the detailed simulation. The proposed simulator generates thousands of particle showers per second on a desktop machine, a speed up of up to 6 orders of magnitudes over \textsc{Geant4}, and stores detailed geometric information about the shower propagation. \textsc{\textsc{SUPA}} provides much greater flexibility for setting initial conditions and defining multiple benchmarks for the development of models. Moreover, interpreting particle showers as point clouds creates a connection to geometric machine learning and provides challenging and fundamentally new datasets for the field.

Applications/Physics

Xiao-Yang Liu, Zeliang Zhang

Google's quantum supremacy announcement has received broad questions from academia and industry due to the debatable estimate of 10,000 years' running time for the classical simulation task on the Summit supercomputer. Has quantum supremacy already come? Or will it come in one or two decades later? To avoid hasty advertisements of quantum supremacy by tech giants or quantum startups and eliminate the cost of dedicating a team to the classical simulation task, we advocate an open-source approach to maintain a trustable benchmark performance. In this paper, we take a reinforcement learning approach for the classical simulation of quantum circuits and demonstrate its great potential by reporting an estimated simulation time of less than 4 days, a speedup of 5.40x over the state-of-the-art method. Specifically, we formulate the classical simulation task as a tensor network contraction ordering problem using the K-spin Ising model and employ a novel Hamiltonina-based reinforcement learning algorithm. Then, we establish standard criteria to evaluate the performance of classical simulation of quantum circuits. We develop a dozen of massively parallel environments to simulate quantum circuits. We open-source our parallel gym environments and benchmarks. We hope the AI/ML community and quantum physics community will collaborate to maintain reference curves for validating an unequivocal first demonstration of empirical quantum supremacy.

Applications/Physics

Mason Wang, Samuel Clarke, Jui-Hsien Wang, Ruohan Gao, Jiajun Wu

A room’s acoustic properties are a product of the room’s geometry, the objects within the room, and their specific positions. A room’s acoustic properties can be characterized by its impulse response (RIR) between a source and listener location, or roughly inferred from recordings of natural signals present in the room. Variations in the positions of objects in a room can effect measurable changes in the room’s acoustic properties, as characterized by the RIR. Existing datasets of RIRs either do not systematically vary positions of objects in an environment, or they consist of only simulated RIRs. We present SoundCam, the largest dataset of unique RIRs from in-the-wild rooms publicly released to date. It includes 5,000 10-channel real-world measurements of room impulse responses and 2,000 10-channel recordings of music in three different rooms, including a controlled acoustic lab, an in-the-wild living room, and a conference room, with different humans in positions throughout each room. We show that these measurements can be used for interesting tasks, such as detecting and identifying humans, and tracking their positions.

Applications/Physics

Benjamin Holzschuh, Simona Vegetti, Nils Thuerey

We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an approximate inverse physics simulator and a learned correction function. A central insight of our work is that training the learned correction with a single-step loss is equivalent to a score matching objective, while recursively predicting longer parts of the trajectory during training relates to maximum likelihood training of a corresponding probability flow.We highlight the advantages of our algorithm compared to standard denoising score matching and implicit score matching, as well as fully learned baselines for a wide range of inverse physics problems. The resulting inverse solver has excellent accuracy and temporal stability and, in contrast to other learned inverse solvers, allows for sampling the posterior of the solutions. Code and experiments are available at https://github.com/tum-pbs/SMDP.

Applications/Physics

Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, Eunbyung Park

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs and approximate very complex solution functions.The number of training points (collocation points) required on these challenging PDEs grows substantially, and it is severely limited due to the expensive computational costs and heavy memory overhead.To overcome this limit, we propose a network architecture and training algorithm for PINNs.The proposed method, separable PINN (SPINN), operates on a per-axis basis to decrease the number of network propagations in multi-dimensional PDEs instead of point-wise processing in conventional PINNs.We also propose using forward-mode automatic differentiation to reduce the computational cost of computing PDE residuals, enabling a large number of collocation points ($>10^7$) on a single commodity GPU. The experimental results show significantly reduced computational costs ($62\times$ in wall-clock time, $1,394\times$ in FLOPs given the same number of collocation points) in multi-dimensional PDEs while achieving better accuracy.Furthermore, we present that SPINN can solve a chaotic (2+1)-d Navier-Stokes equation much faster than the best-performing prior method (9 minutes vs. 10 hours in a single GPU), maintaining accuracy.Finally, we showcase that SPINN can accurately obtain the solution of a highly nonlinear and multi-dimensional PDE, a (3+1)-d Navier-Stokes equation.For visualized results and code, please see https://jwcho5576.github.io/spinn.github.io/.

Applications/Physics

Bogdan Raonic, Roberto Molinaro, Tim De Ryck, Tobias Rohner, Francesca Bartolucci, Rima Alaifari, Siddhartha Mishra, Emmanuel de Bézenac

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is designed specifically to preserve its underlying continuous nature, even when implemented in a discretized form on a computer. We prove a universality theorem to show that CNOs can approximate operators arising in PDEs to desired accuracy. CNOs are tested on a novel suite of benchmarks, encompassing a diverse set of PDEs with multi-scale solutions and are observed to significantly outperform baselines, paving the way for an alternative framework for robust and accurate operator learning.

Applications/Physics

Laurence Midgley, Vincent Stimper, Javier Antorán, Emile Mathieu, Bernhard Schölkopf, José Miguel Hernández-Lobato

Coupling normalizing flows allow for fast sampling and density evaluation, making them the tool of choice for probabilistic modeling of physical systems. However, the standard coupling architecture precludes endowing flows that operate on the Cartesian coordinates of atoms with the SE(3) and permutation invariances of physical systems. This work proposes a coupling flow that preserves SE(3) and permutation equivariance by performing coordinate splits along additional augmented dimensions. At each layer, the flow maps atoms' positions into learned SE(3) invariant bases, where we apply standard flow transformations, such as monotonic rational-quadratic splines, before returning to the original basis.Crucially, our flow preserves fast sampling and density evaluation, and may be used to produce unbiased estimates of expectations with respect to the target distribution via importance sampling.When trained on the DW4, LJ13, and QM9-positional datasets, our flow is competitive with equivariant continuous normalizing flows and diffusion models, while allowing sampling more than an order of magnitude faster.Moreover, to the best of our knowledge, we are the first to learn the full Boltzmann distribution of alanine dipeptide by only modeling the Cartesian positions of its atoms.Lastly, we demonstrate that our flow can be trained to approximately sample from the Boltzmann distribution of the DW4 and LJ13 particle systems using only their energy functions.

Applications/Physics

Jules Berman, Benjamin Peherstorfer

Training neural networks sequentially in time to approximate solution fields of time-dependent partial differential equations can be beneficial for preserving causality and other physics properties; however, the sequential-in-time training is numerically challenging because training errors quickly accumulate and amplify over time. This work introduces Neural Galerkin schemes that update randomized sparse subsets of network parameters at each time step. The randomization avoids overfitting locally in time and so helps prevent the error from accumulating quickly over the sequential-in-time training, which is motivated by dropout that addresses a similar issue of overfitting due to neuron co-adaptation. The sparsity of the update reduces the computational costs of training without losing expressiveness because many of the network parameters are redundant locally at each time step. In numerical experiments with a wide range of evolution equations, the proposed scheme with randomized sparse updates is up to two orders of magnitude more accurate at a fixed computational budget and up to two orders of magnitude faster at a fixed accuracy than schemes with dense updates.

Applications/Physics

Di Luo, Jiayu Shen, Rumen Dangovski, Marin Soljacic

Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman operator theory, which has found utility in applications because it allows for a linear representation of nonlinear dynamical systems, and natural gradient methods in quantum optimization, leading to a significant acceleration of gradient-based quantum optimization. We present Quantum-circuit Alternating Controlled Koopman learning (QuACK), a novel framework that leverages an alternating algorithm for efficient prediction of gradient dynamics on quantum computers. We demonstrate QuACK's remarkable ability to accelerate gradient-based optimization across a range of applications in quantum optimization and machine learning. In fact, our empirical studies, spanning quantum chemistry, quantum condensed matter, quantum machine learning, and noisy environments, have shown accelerations of more than 200x speedup in the overparameterized regime, 10x speedup in the smooth regime, and 3x speedup in the non-smooth regime. With QuACK, we offer a robust advancement that harnesses the advantage of gradient-based quantum optimization for practical benefits.