NeurIPS 2023 Papers

Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these scientific problems, molecules serve as the fundamental building blocks, and machine learning has emerged as a highly effective and powerful tool for modeling their geometric structures. Nevertheless, due to the rapidly evolving process of the field and the knowledge gap between science ({\eg}, physics, chemistry, \& biology) and machine learning communities, a benchmarking study on geometrical representation for such data has not been conducted. To address such an issue, in this paper, we first provide a unified view of the current symmetry-informed geometric methods, classifying them into three main categories: invariance, equivariance with spherical frame basis, and equivariance with vector frame basis. Then we propose a platform, coined Geom3D, which enables benchmarking the effectiveness of geometric strategies. Geom3D contains 16 advanced symmetry-informed geometric representation models and 14 geometric pretraining methods over 52 diverse tasks, including small molecules, proteins, and crystalline materials. We hope that Geom3D can, on the one hand, eliminate barriers for machine learning researchers interested in exploring scientific problems; and, on the other hand, provide valuable guidance for researchers in computational chemistry, structural biology, and materials science, aiding in the informed selection of representation techniques for specific applications. The source code is available on \href{https://github.com/chao1224/Geom3D}{the GitHub repository}.

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.

Confidence calibration is central to providing accurate and interpretable uncertainty estimates, especially under safety-critical scenarios. However, we find that existing calibration algorithms often overlook the issue of proximity bias, a phenomenon where models tend to be more overconfident in low proximity data (i.e., data lying in the sparse region of the data distribution) compared to high proximity samples, and thus suffer from inconsistent miscalibration across different proximity samples. We examine the problem over $504$ pretrained ImageNet models and observe that: 1) Proximity bias exists across a wide variety of model architectures and sizes; 2) Transformer-based models are relatively more susceptible to proximity bias than CNN-based models; 3) Proximity bias persists even after performing popular calibration algorithms like temperature scaling; 4) Models tend to overfit more heavily on low proximity samples than on high proximity samples. Motivated by the empirical findings, we propose ProCal, a plug-and-play algorithm with a theoretical guarantee to adjust sample confidence based on proximity. To further quantify the effectiveness of calibration algorithms in mitigating proximity bias, we introduce proximity-informed expected calibration error (PIECE) with theoretical analysis. We show that ProCal is effective in addressing proximity bias and improving calibration on balanced, long-tail, and distribution-shift settings under four metrics over various model architectures. We believe our findings on proximity bias will guide the development of fairer and better-calibrated} models, contributing to the broader pursuit of trustworthy AI.

We introduce a novel policy learning method that integrates analytical gradients from differentiable environments with the Proximal Policy Optimization (PPO) algorithm. To incorporate analytical gradients into the PPO framework, we introduce the concept of an α-policy that stands as a locally superior policy. By adaptively modifying the α value, we can effectively manage the influence of analytical policy gradients during learning. To this end, we suggest metrics for assessing the variance and bias of analytical gradients, reducing dependence on these gradients when high variance or bias is detected. Our proposed approach outperforms baseline algorithms in various scenarios, such as function optimization, physics simulations, and traffic control environments. Our code can be found online: https://github.com/SonSang/gippo.

Human hands possess remarkable dexterity and have long served as a source of inspiration for robotic manipulation. In this work, we propose a human $\textbf{H}$and-$\textbf{In}$formed visual representation learning framework to solve difficult $\textbf{Dex}$terous manipulation tasks ($\textbf{H-InDex}$) with reinforcement learning. Our framework consists of three stages: $\textit{(i)}$ pre-training representations with 3D human hand pose estimation, $\textit{(ii)}$ offline adapting representations with self-supervised keypoint detection, and $\textit{(iii)}$ reinforcement learning with exponential moving average BatchNorm. The last two stages only modify $0.36$% parameters of the pre-trained representation in total, ensuring the knowledge from pre-training is maintained to the full extent. We empirically study $\textbf{12}$ challenging dexterous manipulation tasks and find that $\textbf{H-InDex}$ largely surpasses strong baseline methods and the recent visual foundation models for motor control. Code and videos are available at https://yanjieze.com/H-InDex .

We study recovering fluid density and velocity from sparse multiview videos. Existing neural dynamic reconstruction methods predominantly rely on optical flows; therefore, they cannot accurately estimate the density and uncover the underlying velocity due to the inherent visual ambiguities of fluid velocity, as fluids are often shapeless and lack stable visual features. The challenge is further pronounced by the turbulent nature of fluid flows, which calls for properly designed fluid velocity representations. To address these challenges, we propose hybrid neural fluid fields (HyFluid), a neural approach to jointly infer fluid density and velocity fields. Specifically, to deal with visual ambiguities of fluid velocity, we introduce a set of physics-based losses that enforce inferring a physically plausible velocity field, which is divergence-free and drives the transport of density. To deal with the turbulent nature of fluid velocity, we design a hybrid neural velocity representation that includes a base neural velocity field that captures most irrotational energy and a vortex particle-based velocity that models residual turbulent velocity. We show that our method enables recovering vortical flow details. Our approach opens up possibilities for various learning and reconstruction applications centered around 3D incompressible flow, including fluid re-simulation and editing, future prediction, and neural dynamic scene composition. Project website: https://kovenyu.com/HyFluid/

As a classical generative modeling approach, energy-based models have the natural advantage of flexibility in the form of the energy function. Recently, energy-based models have achieved great success in modeling high-dimensional data in computer vision and natural language processing. In line with these advancements, we build a multi-purpose energy-based probabilistic model for High Energy Physics events at the Large Hadron Collider. This framework builds on a powerful generative model and describes higher-order inter-particle interactions. It suits different encoding architectures and builds on implicit generation. As for applicative aspects, it can serve as a powerful parameterized event generator for physics simulation, a generic anomalous signal detector free from spurious correlations, and an augmented event classifier for particle identification.

Generating animation of physics-based characters with intuitive control has long been a desirable task with numerous applications. However, generating physically simulated animations that reflect high-level human instructions remains a difficult problem due to the complexity of physical environments and the richness of human language. In this paper, we present $\textbf{InsActor}$, a principled generative framework that leverages recent advancements in diffusion-based human motion models to produce instruction-driven animations of physics-based characters. Our framework empowers InsActor to capture complex relationships between high-level human instructions and character motions by employing diffusion policies for flexibly conditioned motion planning. To overcome invalid states and infeasible state transitions in planned motions, InsActor discovers low-level skills and maps plans to latent skill sequences in a compact latent space. Extensive experiments demonstrate that InsActor achieves state-of-the-art results on various tasks, including instruction-driven motion generation and instruction-driven waypoint heading. Notably, the ability of InsActor to generate physically simulated animations using high-level human instructions makes it a valuable tool, particularly in executing long-horizon tasks with a rich set of instructions. Our project page is available at [jiawei-ren.github.io/projects/insactor/index.html](https://jiawei-ren.github.io/projects/insactor/index.html)

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design parameters) and solvers are required to perform rapid execution. In this study, we suggest a path that potentially opens up a possibility for physics-informed neural networks (PINNs), emerging deep-learning-based solvers, to be considered as one such solver. Although PINNs have pioneered a proper integration of deep-learning and scientific computing, they require repetitive time-consuming training of neural networks, which is not suitable for many-query scenarios. To address this issue, we propose a lightweight low-rank PINNs containing only hundreds of model parameters and an associated hypernetwork-based meta-learning algorithm, which allows efficient approximation of solutions of PDEs for varying ranges of PDE input parameters. Moreover, we show that the proposed method is effective in overcoming a challenging issue, known as "failure modes" of PINNs.

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/.

Nowadays integrated circuits (ICs) are underpinning all major information technology innovations including the current trends of artificial intelligence (AI). Modern IC designs often involve analyses of complex phenomena (such as timing, noise, and power etc.) for tens of billions of electronic components, like resistance (R), capacitance (C), transistors and gates, interconnected in various complex structures. Those analyses often need to strike a balance between accuracy and speed as those analyses need to be carried out many times throughout the entire IC design cycles. With the advancement of AI, researchers also start to explore news ways in leveraging AI to improve those analyses. This paper focuses on one of the most important analyses, timing analysis for interconnects. Since IC interconnects can be represented as an RC-tree, a specialized graph as tree, we design a novel tree-based graph neural network, SyncTREE, to speed up the timing analysis by incorporating both the structural and physical properties of electronic circuits. Our major innovations include (1) a two-pass message-passing (bottom-up and top-down) for graph embedding, (2) a tree contrastive loss to guide learning, and (3) a closed formular-based approach to conduct fast timing. Our experiments show that, compared to conventional GNN models, SyncTREE achieves the best timing prediction in terms of both delays and slews, all in reference to the industry golden numerical analyses results on real IC design data.

Symmetries have been leveraged to improve the generalization of neural networks through different mechanisms from data augmentation to equivariant architectures. However, despite their potential, their integration into neural solvers for partial differential equations (PDEs) remains largely unexplored. We explore the integration of PDE symmetries, known as Lie point symmetries, in a major family of neural solvers known as physics-informed neural networks (PINNs). We propose a loss function that informs the network about Lie point symmetries in the same way that PINN models try to enforce the underlying PDE through a loss function. Intuitively, our symmetry loss ensures that the infinitesimal generators of the Lie group conserve the PDE solutions.. Effectively, this means that once the network learns a solution, it also learns the neighbouring solutions generated by Lie point symmetries. Empirical evaluations indicate that the inductive bias introduced by the Lie point symmetries of the PDEs greatly boosts the sample efficiency of PINNs.

Engineering design problems frequently require solving systems of partial differential equations with boundary conditions specified on object geometries in the form of a triangular mesh. These boundary geometries are provided by a designer and are problem dependent. The efficiency of the design process greatly benefits from fast turnaround times when repeatedly solving PDEs on various geometries. However, most current work that uses machine learning to speed up the solution process relies heavily on a fixed parameterization of the geometry, which cannot be changed after training. This severely limits the possibility of reusing a trained model across a variety of design problems. In this work, we propose a novel neural operator architecture which accepts boundary geometry, in the form of triangular meshes, as input and produces an approximate solution to a given PDE as output. Once trained, the model can be used to rapidly estimate the PDE solution over a new geometry, without the need for retraining or representation of the geometry to a pre-specified parameterization.

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints. A consequence is inaccurate and imprecise predictions of critical processes such as storms. Hybrid methods that combine physics with machine learning (ML) have introduced a new generation of higher fidelity climate simulators that can sidestep Moore's Law by outsourcing compute-hungry, short, high-resolution simulations to ML emulators. However, this hybrid ML-physics simulation approach requires domain-specific treatment and has been inaccessible to ML experts because of lack of training data and relevant, easy-to-use workflows. We present ClimSim, the largest-ever dataset designed for hybrid ML-physics research. It comprises multi-scale climate simulations, developed by a consortium of climate scientists and ML researchers. It consists of 5.7 billion pairs of multivariate input and output vectors that isolate the influence of locally-nested, high-resolution, high-fidelity physics on a host climate simulator's macro-scale physical state. The dataset is global in coverage, spans multiple years at high sampling frequency, and is designed such that resulting emulators are compatible with downstream coupling into operational climate simulators. We implement a range of deterministic and stochastic regression baselines to highlight the ML challenges and their scoring. The data (https://huggingface.co/datasets/LEAP/ClimSim_high-res) and code (https://leap-stc.github.io/ClimSim) are released openly to support the development of hybrid ML-physics and high-fidelity climate simulations for the benefit of science and society.

Magnetic Resonance Imaging (MRI) is a powerful medical imaging modality that offers diagnostic information without harmful ionizing radiation. Unlike optical imaging, MRI sequentially samples the spatial Fourier domain (k-space) of the image. Measurements are collected in multiple shots, or readouts, and in each shot, data along a smooth trajectory is sampled. Conventional MRI data acquisition relies on sampling k-space row-by-row in short intervals, which is slow and inefficient. More efficient, non-Cartesian sampling trajectories (e.g., Spirals) use longer data readout intervals, but are more susceptible to magnetic field inhomogeneities, leading to off-resonance artifacts. Spiral trajectories cause off-resonance blurring in the image, and the mathematics of this blurring resembles that of optical blurring, where magnetic field variation corresponds to depth and readout duration to aperture size. Off-resonance blurring is a system issue with a physics-based, accurate forward model. We present a physics-informed deep learning framework for off-resonance correction in MRI, which is trained exclusively on synthetic, noise-like data with representative marginal statistics. Our approach allows for fat/water separation and is compatible with parallel imaging acceleration. Through end-to-end training using synthetic randomized data (i.e., noise-like images, coil sensitivities, field maps), we train the network to reverse off-resonance effects across diverse anatomies and contrasts without retraining. We demonstrate the effectiveness of our approach through results on phantom and in-vivo data. This work has the potential to facilitate the clinical adoption of non-Cartesian sampling trajectories, enabling efficient, rapid, and motion-robust MRI scans. Code is publicly available at: https://github.com/mikgroup/ResoNet.

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.

Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations. Indicatively, strong assumptions regarding the data likelihood are required, the performance highly depends on the selection of priors, and the posterior can be sampled only approximately, which leads to poor approximations because of the associated computational cost. This paper introduces and studies confidence interval (CI) estimation for deterministic partial differential equations as a novel problem. That is, to propagate confidence, in the form of CIs, from data locations to the entire domain with probabilistic guarantees. We propose a method, termed Physics-Informed Confidence Propagation (PICProp), based on bi-level optimization to compute a valid CI without making heavy assumptions. We provide a theorem regarding the validity of our method, and computational experiments, where the focus is on physics-informed learning. Code is available at https://github.com/ShenQianli/PICProp.

When deploying machine learning estimators in science and engineering (SAE) domains, it is critical to avoid failed estimations that can have disastrous consequences, e.g., in aero engine design. This work focuses on detecting and correcting failed state estimations before adopting them in SAE inverse problems, by utilizing simulations and performance metrics guided by physical laws. We suggest to flag a machine learning estimation when its physical model error exceeds a feasible threshold, and propose a novel approach, GEESE, to correct it through optimization, aiming at delivering both low error and high efficiency. The key designs of GEESE include (1) a hybrid surrogate error model to provide fast error estimations to reduce simulation cost and to enable gradient based backpropagation of error feedback, and (2) two generative models to approximate the probability distributions of the candidate states for simulating the exploitation and exploration behaviours. All three models are constructed as neural networks. GEESE is tested on three real-world SAE inverse problems and compared to a number of state-of-the-art optimization/search approaches. Results show that it fails the least number of times in terms of finding a feasible state correction, and requires physical evaluations less frequently in general.

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.