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Applications/Physics

Xihan Li, Xiang Chen, Rasul Tutunov, Haitham Bou Ammar, Lei Wang, Jun Wang

Self-consistent Field (SCF) equation is a type of nonlinear eigenvalue problem in which the matrix to be eigen-decomposed is a function of its own eigenvectors. It is of great significance in computational science for its connection to the Schrödinger equation. Traditional fixed-point iteration methods for solving such equations suffer from non-convergence issues. In this work, we present a novel perspective on such SCF equations as a principal component analysis (PCA) for non-stationary time series, in which a distribution and its own top principal components are mutually updated over time, and the equilibrium state of the model corresponds to the solution of the SCF equations. By the new perspective, online PCA techniques are able to engage in so as to enhance the convergence of the model towards the equilibrium state, acting as a new set of tools for converging the SCF equations. With several numerical adaptations, we then develop a new algorithm for converging the SCF equation, and demonstrated its high convergence capacity with experiments on both synthesized and real electronic structure scenarios.

Deep Learning/Graph Neural Networks

Zun Wang, Guoqing Liu, Yichi Zhou, Tong Wang, Bin Shao

Machine learning force fields (MLFFs) have instigated a groundbreaking shift in molecular dynamics (MD) simulations across a wide range of fields, such as physics, chemistry, biology, and materials science. Incorporating higher order many-body interactions can enhance the expressiveness and accuracy of models. Recent models have achieved this by explicitly including up to four-body interactions. However, five-body interactions, which have relevance in various fields, are still challenging to incorporate efficiently into MLFFs. In this work, we propose the quintuple network (QuinNet), an end-to-end graph neural network that efficiently expresses many-body interactions up to five-body interactions with \emph{ab initio} accuracy. By analyzing the topology of diverse many-body interactions, we design the model architecture to efficiently and explicitly represent these interactions. We evaluate QuinNet on public datasets of small molecules, such as MD17 and its revised version, and show that it is compatible with other state-of-the-art models on these benchmarks. Moreover, QuinNet surpasses many leading models on larger and more complex molecular systems, such as MD22 and Chignolin, without increasing the computational complexity. We also use QuinNet as a force field for molecular dynamics (MD) simulations to demonstrate its accuracy and stability, and conduct an ablation study to elucidate the significance of five-body interactions. We open source our implementation at https://github.com/Zun-Wang/QuinNet.

Applications/Physics

Leon Klein, Andreas Krämer, Frank Noe

Normalizing flows are a class of deep generative models that are especially interesting for modeling probability distributions in physics, where the exact likelihood of flows allows reweighting to known target energy functions and computing unbiased observables. For instance, Boltzmann generators tackle the long-standing sampling problem in statistical physics by training flows to produce equilibrium samples of many-body systems such as small molecules and proteins. To build effective models for such systems, it is crucial to incorporate the symmetries of the target energy into the model, which can be achieved by equivariant continuous normalizing flows (CNFs). However, CNFs can be computationally expensive to train and generate samples from, which has hampered their scalability and practical application.In this paper, we introduce equivariant flow matching, a new training objective for equivariant CNFs that is based on the recently proposed optimal transport flow matching. Equivariant flow matching exploits the physical symmetries of the target energy for efficient, simulation-free training of equivariant CNFs.We demonstrate the effectiveness of flow matching on rotation and permutation invariant many-particle systems and a small molecule, alanine dipeptide, where for the first time we obtain a Boltzmann generator with significant sampling efficiency without relying on tailored internal coordinate featurization. Our results show that the equivariant flow matching objective yields flows with shorter integration paths, improved sampling efficiency, and higher scalability compared to existing methods.

Applications/Everything Else

Jialv Zou, Xinggang Wang, Jiahao Guo, Wenyu Liu, Qian Zhang, Chang Huang

As the size of circuit designs continues to grow rapidly, artificial intelligence technologies are being extensively used in Electronic Design Automation (EDA) to assist with circuit design.Placement and routing are the most time-consuming parts of the physical design process, and how to quickly evaluate the placement has become a hot research topic. Prior works either transformed circuit designs into images using hand-crafted methods and then used Convolutional Neural Networks (CNN) to extract features, which are limited by the quality of the hand-crafted methods and could not achieve end-to-end training, or treated the circuit design as a graph structure and used Graph Neural Networks (GNN) to extract features, which require time-consuming preprocessing.In our work, we propose a novel perspective for circuit design by treating circuit components as point clouds and using Transformer-based point cloud perception methods to extract features from the circuit. This approach enables direct feature extraction from raw data without any preprocessing, allows for end-to-end training, and results in high performance.Experimental results show that our method achieves state-of-the-art performance in congestion prediction tasks on both the CircuitNet and ISPD2015 datasets, as well as in design rule check (DRC) violation prediction tasks on the CircuitNet dataset.Our method establishes a bridge between the relatively mature point cloud perception methods and the fast-developing EDA algorithms, enabling us to leverage more collective intelligence to solve this task. To facilitate the research of open EDA design, source codes and pre-trained models are released at https://github.com/hustvl/circuitformer.

Deep Learning/Graph Neural Networks

David Ruhe, Johannes Brandstetter, Patrick Forré

We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the *Clifford group*: a subgroup inside the Clifford algebra tailored to achieve several favorable properties. Primarily, the group's action forms an orthogonal automorphism that extends beyond the typical vector space to the entire Clifford algebra while respecting the multivector grading. This leads to several non-equivalent subrepresentations corresponding to the multivector decomposition. Furthermore, we prove that the action respects not just the vector space structure of the Clifford algebra but also its multiplicative structure, i.e., the geometric product. These findings imply that every polynomial in multivectors, including their grade projections, constitutes an equivariant map with respect to the Clifford group, allowing us to parameterize equivariant neural network layers. An advantage worth mentioning is that we obtain expressive layers that can elegantly generalize to inner-product spaces of any dimension. We demonstrate, notably from a single core implementation, state-of-the-art performance on several distinct tasks, including a three-dimensional $n$-body experiment, a four-dimensional Lorentz-equivariant high-energy physics experiment, and a five-dimensional convex hull experiment.

Probabilistic Methods/Bayesian Models and Methods

Theo Gruner, Boris Belousov, Fabio Muratore, Daniel Palenicek, Jan Peters

Simulation-Based Inference (SBI) is a common name for an emerging family of approaches that infer the model parameters when the likelihood is intractable. Existing SBI methods either approximate the likelihood, such as Approximate Bayesian Computation (ABC) or directly model the posterior, such as Sequential Neural Posterior Estimation (SNPE). While ABC is efficient on low-dimensional problems, on higher-dimensional tasks, it is generally outperformed by SNPE, which leverages function approximation. In this paper, we propose Pseudo-Likelihood Inference (PLI), a new method that brings neural approximation into ABC, making it competitive on challenging Bayesian system identification tasks. By utilizing integral probability metrics, we introduce a smooth likelihood kernel with an adaptive bandwidth that is updated based on information-theoretic trust regions. Thanks to this formulation, our method (i) allows for optimizing neural posteriors via gradient descent, (ii) does not rely on summary statistics, and (iii) enables multiple observations as input. In comparison to SNPE, it leads to improved performance when more data is available. The effectiveness of PLI is evaluated on four classical SBI benchmark tasks and on a highly dynamic physical system, showing particular advantages on stochastic simulations and multi-modal posterior landscapes.

Scott Cameron, Arnu Pretorius, S Roberts

Engineering design problems frequently require solving systems ofpartial differential equations with boundary conditions specified onobject geometries in the form of a triangular mesh. These boundarygeometries are provided by a designer and are problem dependent.The efficiency of the design process greatly benefits from fast turnaroundtimes when repeatedly solving PDEs on various geometries. However,most current work that uses machine learning to speed up the solutionprocess relies heavily on a fixed parameterization of the geometry, whichcannot be changed after training. This severely limits the possibility ofreusing a trained model across a variety of design problems.In this work, we propose a novel neural operator architecture which acceptsboundary geometry, in the form of triangular meshes, as input and produces anapproximate solution to a given PDE as output. Once trained, the model can beused to rapidly estimate the PDE solution over a new geometry, without the need forretraining or representation of the geometry to a pre-specified parameterization.

Applications/Physics

Ning Liu, Siavash Jafarzadeh, Yue Yu

Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs rely on the Fast Fourier transform (FFT), which is restricted to modeling problems on rectangular domains. To lift such a restriction and permit FFT on irregular geometries as well as topology changes, we introduce domain agnostic Fourier neural operator (DAFNO), a novel neural operator architecture for learning surrogates with irregular geometries and evolving domains. The key idea is to incorporate a smoothed characteristic function in the integral layer architecture of FNOs, and leverage FFT to achieve rapid computations, in such a way that the geometric information is explicitly encoded in the architecture. In our empirical evaluation, DAFNO has achieved state-of-the-art accuracy as compared to baseline neural operator models on two benchmark datasets of material modeling and airfoil simulation. To further demonstrate the capability and generalizability of DAFNO in handling complex domains with topology changes, we consider a brittle material fracture evolution problem. With only one training crack simulation sample, DAFNO has achieved generalizability to unseen loading scenarios and substantially different crack patterns from the trained scenario. Our code and data accompanying this paper are available at https://github.com/ningliu-iga/DAFNO.

Applications/Physics

Zijie Li, Dule Shu, Amir Barati Farimani

Transformer has shown state-of-the-art performance on various applications and has recently emerged as a promising tool for surrogate modeling of partial differential equations (PDEs). Despite the introduction of linear-complexity attention, applying Transformer to problems with a large number of grid points can be numerically unstable and computationally expensive. In this work, we propose Factorized Transformer (FactFormer), which is based on an axial factorized kernel integral. Concretely, we introduce a learnable projection operator that decomposes the input function into multiple sub-functions with one-dimensional domain. These sub-functions are then evaluated and used to compute the instance-based kernel with an axial factorized scheme. We showcase that the proposed model is able to simulate 2D Kolmogorov flow on a $256\times 256$ grid and 3D smoke buoyancy on a $64\times64\times64$ grid with good accuracy and efficiency. The proposed factorized scheme can serve as a computationally efficient low-rank surrogate for the full attention scheme when dealing with multi-dimensional problems.

Probabilistic Methods/Bayesian Models and Methods

Kim Nicoli, Christopher J. Anders, Lena Funcke, Tobias Hartung, Karl Jansen, Stefan Kühn, Klaus-Robert Müller, Paolo Stornati, Pan Kessel, Shinichi Nakajima

In this paper, we propose a novel and powerful method to harness Bayesian optimization for variational quantum eigensolvers (VQEs) - a hybrid quantum-classical protocol used to approximate the ground state of a quantum Hamiltonian. Specifically, we derive a *VQE-kernel* which incorporates important prior information about quantum circuits: the kernel feature map of the VQE-kernel exactly matches the known functional form of the VQE's objective function and thereby significantly reduces the posterior uncertainty.Moreover, we propose a novel acquisition function for Bayesian optimization called \emph{Expected Maximum Improvement over Confident Regions} (EMICoRe) which can actively exploit the inductive bias of the VQE-kernel by treating regions with low predictive uncertainty as indirectly "observed". As a result, observations at as few as three points in the search domain are sufficient to determine the complete objective function along an entire one-dimensional subspace of the optimization landscape. Our numerical experiments demonstrate that our approach improves over state-of-the-art baselines.

Applications/Physics

Kirill Neklyudov, Jannes Nys, Luca Thiede, Juan Carrasquilla, Qiang Liu, Max Welling, Alireza Makhzani

Solving the quantum many-body Schrödinger equation is a fundamental and challenging problem in the fields of quantum physics, quantum chemistry, and material sciences. One of the common computational approaches to this problem is Quantum Variational Monte Carlo (QVMC), in which ground-state solutions are obtained by minimizing the energy of the system within a restricted family of parameterized wave functions. Deep learning methods partially address the limitations of traditional QVMC by representing a rich family of wave functions in terms of neural networks. However, the optimization objective in QVMC remains notoriously hard to minimize and requires second-order optimization methods such as natural gradient. In this paper, we first reformulate energy functional minimization in the space of Born distributions corresponding to particle-permutation (anti-)symmetric wave functions, rather than the space of wave functions. We then interpret QVMC as the Fisher--Rao gradient flow in this distributional space, followed by a projection step onto the variational manifold. This perspective provides us with a principled framework to derive new QMC algorithms, by endowing the distributional space with better metrics, and following the projected gradient flow induced by those metrics. More specifically, we propose "Wasserstein Quantum Monte Carlo" (WQMC), which uses the gradient flow induced by the Wasserstein metric, rather than the Fisher--Rao metric, and corresponds to *transporting* the probability mass, rather than *teleporting* it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.

Deep Learning/Graph Neural Networks

Anthony Gruber, Kookjin Lee, Nathaniel Trask

Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear, however, with successful examples of both reversible (e.g., Hamiltonian) and irreversible (e.g., diffusion) phenomena producing comparable results despite diametrically opposed mechanisms, and further complications arising due to empirical departures from mathematical theory. This work presents a series of novel GNN architectures based upon structure-preserving bracket-based dynamical systems, which are provably guaranteed to either conserve energy or generate positive dissipation with increasing depth. It is shown that the theoretically principled framework employed here allows for inherently explainable constructions, which contextualize departures from theory in current architectures and better elucidate the roles of reversibility and irreversibility in network performance. Code is available at the Github repository \url{https://github.com/natrask/BracketGraphs}.

Applications/Physics

Krzysztof Kacprzyk, Zhaozhi Qian, Mihaela van der Schaar

Closed-form differential equations, including partial differential equations and higher-order ordinary differential equations, are one of the most important tools used by scientists to model and better understand natural phenomena. Discovering these equations directly from data is challenging because it requires modeling relationships between various derivatives that are not observed in the data (equation-data mismatch) and it involves searching across a huge space of possible equations. Current approaches make strong assumptions about the form of the equation and thus fail to discover many well-known phenomena. Moreover, many of them resolve the equation-data mismatch by estimating the derivatives, which makes them inadequate for noisy and infrequent observations. To this end, we propose D-CIPHER, which is robust to measurement artifacts and can uncover a new and very general class of differential equations. We further design a novel optimization procedure, CoLLie, to help D-CIPHER search through this class efficiently. Finally, we demonstrate empirically that it can discover many well-known equations that are beyond the capabilities of current methods.

Applications/Language, Speech and Dialog

Allen Nie, Yuhui Zhang, Atharva Shailesh Amdekar, Chris Piech, Tatsunori Hashimoto, Tobias Gerstenberg

Human commonsense understanding of the physical and social world is organized around intuitive theories. These theories support making causal and moral judgments. When something bad happens, we naturally ask: who did what, and why? A rich literature in cognitive science has studied people's causal and moral intuitions. This work has revealed a number of factors that systematically influence people's judgments, such as the violation of norms and whether the harm is avoidable or inevitable. We collected a dataset of stories from 24 cognitive science papers and developed a system to annotate each story with the factors they investigated. Using this dataset, we test whether large language models (LLMs) make causal and moral judgments about text-based scenarios that align with those of human participants. On the aggregate level, alignment has improved with more recent LLMs. However, using statistical analyses, we find that LLMs weigh the different factors quite differently from human participants. These results show how curated, challenge datasets combined with insights from cognitive science can help us go beyond comparisons based merely on aggregate metrics: we uncover LLMs implicit tendencies and show to what extent these align with human intuitions.

Applications/Chemistry and Drug Discovery

Sergey Pozdnyakov, Michele Ceriotti

Point clouds are versatile representations of 3D objects and have found widespread application in science and engineering. Many successful deep-learning models have been proposed that use them as input. The domain of chemical and materials modeling is especially challenging because exact compliance with physical constraints is highly desirable for a model to be usable in practice. These constraints include smoothness and invariance with respect to translations, rotations, and permutations of identical atoms. If these requirements are not rigorously fulfilled, atomistic simulations might lead to absurd outcomes even if the model has excellent accuracy. Consequently, dedicated architectures, which achieve invariance by restricting their design space, have been developed. General-purpose point-cloud models are more varied but often disregard rotational symmetry. We propose a general symmetrization method that adds rotational equivariance to any given model while preserving all the other requirements.Our approach simplifies the development of better atomic-scale machine-learning schemes by relaxing the constraints on the design space and making it possible to incorporate ideas that proved effective in other domains.We demonstrate this idea by introducing the Point Edge Transformer (PET) architecture, which is not intrinsically equivariant but achieves state-of-the-art performance on several benchmark datasets of molecules and solids. A-posteriori application of our general protocol makes PET exactly equivariant, with minimal changes to its accuracy.

Qiyu Dai, Jiyao Zhang, Qiwei Li, Tianhao Wu, Hao Dong, Ziyuan Liu, Ping Tan, He Wang

Commercial depth sensors usually generate noisy and missing depths, especially on specular and transparent objects, which poses critical issues to downstream depth or point cloud-based tasks. To mitigate this problem, we propose a powerful RGBD fusion network, SwinDRNet, for depth restoration. We further propose Domain Randomization-Enhanced Depth Simulation (DREDS) approach to simulate an active stereo depth system using physically based rendering and generate a large-scale synthetic dataset that contains 130K photorealistic RGB images along with their simulated depths carrying realistic sensor noises. To evaluate depth restoration methods, we also curate a real-world dataset, namely STD, that captures 30 cluttered scenes composed of 50 objects with different materials from specular, transparent, to diffuse. Experiments demonstrate that the proposed DREDS dataset bridges the sim-to-real domain gap such that, trained on DREDS, our SwinDRNet can seamlessly generalize to other real depth datasets, e.g. ClearGrasp, and outperform the competing methods on depth restoration. We further show that our depth restoration effectively boosts the performance of downstream tasks, including category-level pose estimation and grasping tasks. Our data and code are available at https://github.com/PKU-EPIC/DREDS.

Colton Stearns, Davis Rempe, Jie Li, Rareș Ambruș, Sergey Zakharov, Vitor Guizilini, Yanchao Yang, Leonidas J. Guibas

3D multi-object tracking aims to uniquely and consistently identify all mobile entities through time. Despite the rich spatiotemporal information available in this setting, current 3D tracking methods primarily rely on abstracted information and limited history, e.g. single-frame object bounding boxes. In this work, we develop a holistic representation of traffic scenes that leverages both spatial and temporal information of the actors in the scene. Specifically, we reformulate tracking as a spatiotemporal problem by representing tracked objects as sequences of time-stamped points and bounding boxes over a long temporal history. At each timestamp, we improve the location and motion estimates of our tracked objects through learned refinement over the full sequence of object history. By considering time and space jointly, our representation naturally encodes fundamental physical priors such as object permanence and consistency across time. Our spatiotemporal tracking framework achieves state-of-the-art performance on the Waymo and nuScenes benchmarks.

Zhiyuan Cheng, James Liang, Hongjun Choi, Guanhong Tao, Zhiwen Cao, Dongfang Liu, Xiangyu Zhang

Deep learning has substantially boosted the performance of Monocular Depth Estimation (MDE), a critical component in fully vision-based autonomous driving (AD) systems (e.g., Tesla and Toyota). In this work, we develop an attack against learning-based MDE. In particular, we use an optimization-based method to systematically generate stealthy physical-object-oriented adversarial patches to attack depth estimation. We balance the stealth and effectiveness of our attack with object-oriented adversarial design, sensitive region localization, and natural style camouflage. Using real-world driving scenarios, we evaluate our attack on concurrent MDE models and a representative downstream task for AD (i.e., 3D object detection). Experimental results show that our method can generate stealthy, effective, and robust adversarial patches for different target objects and models and achieves more than 6 meters mean depth estimation error and 93% attack success rate (ASR) in object detection with a patch of 1/9 of the vehicle’s rear area. Field tests on three different driving routes with a real vehicle indicate that we cause over 6 meters mean depth estimation error and reduce the object detection rate from 90.70% to 5.16% in continuous video frames.

Chenfeng Xu, Shijia Yang, Tomer Galanti, Bichen Wu, Xiangyu Yue, Bohan Zhai, Wei Zhan, Peter Vajda, Kurt Keutzer, Masayoshi Tomizuka

3D point-clouds and 2D images are different visual representations of the physical world. While human vision can understand both representations, computer vision models designed for 2D image and 3D point-cloud understanding are quite different. Our paper explores the potential of transferring 2D model architectures and weights to understand 3D point-clouds, by empirically investigating the feasibility of the transfer, the benefits of the transfer, and shedding light on why the transfer works. We discover that we can indeed use the same architecture and pretrained weights of a neural net model to understand both images and point-clouds. Specifically, we transfer the image-pretrained model to a point-cloud model by copying or inflating the weights. We find that finetuning the transformed image-pretrained models (FIP) with minimal efforts --- only on input, output, and normalization layers --- can achieve competitive performance on 3D point-cloud classification, beating a wide range of point-cloud models that adopt task-specific architectures and use a variety of tricks. When finetuning the whole model, the performance gets further improved. Meanwhile, FIP improves data efficiency, reaching up to 10.0 top-1 accuracy percent on few-shot classification. It also speeds up training of point-cloud models by up to 11.1x for a target accuracy (e.g., 90 % accuracy). Lastly, we provide an explanation of the image to point-cloud transfer from the aspect of neural collapse.

Samuel Yu, Peter Wu, Paul Pu Liang, Ruslan Salakhutdinov, Louis-Philippe Morency

In order for AI to be safely deployed in real-world scenarios such as hospitals, schools, and the workplace, it must be able to robustly reason about the physical world. Fundamental to this reasoning is physical common sense: understanding the physical properties and affordances of available objects, how they can be manipulated, and how they interact with other objects. Physical commonsense reasoning is fundamentally a multi-sensory task, since physical properties are manifested through multiple modalities - two of them being vision and acoustics. Our paper takes a step towards real-world physical commonsense reasoning by contributing PACS: the first audiovisual benchmark annotated for physical commonsense attributes. PACS contains 13,400 question-answer pairs, involving 1,377 unique physical commonsense questions and 1,526 videos. Our dataset provides new opportunities to advance the research field of physical reasoning by bringing audio as a core component of this multimodal problem. Using PACS, we evaluate multiple state-of-the-art models on our new challenging task. While some models show promising results (70% accuracy), they all fall short of human performance (95% accuracy). We conclude the paper by demonstrating the importance of multimodal reasoning and providing possible avenues for future research.