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Physical Models

Md Ashiqur Rahman, Robert Joseph George, Mogab Elleithy, Daniel Leibovici, Zongyi Li, Boris Bonev, Colin White, Julius Berner, Raymond A. Yeh, Jean Kossaifi 等

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data. To address these issues, we propose *Codomain Attention Neural Operator* (CoDA-NO), which tokenizes functions along the codomain or channel space, enabling self-supervised learning or pretraining of multiple PDE systems. Specifically, we extend positional encoding, self-attention, and normalization layers to function spaces. CoDA-NO can learn representations of different PDE systems with a single model. We evaluate CoDA-NO's potential as a backbone for learning multiphysics PDEs over multiple systems by considering few-shot learning settings. On complex downstream tasks with limited data, such as fluid flow simulations, fluid-structure interactions, and Rayleigh-Bénard convection, we found CoDA-NO to outperform existing methods by over 36%.

Optimization · Learning for Optimization

Qijian Zhang, Junhui Hou, Wenping Wang, Ying He

Surface parameterization plays an essential role in numerous computer graphics and geometry processing applications. Traditional parameterization approaches are designed for high-quality meshes laboriously created by specialized 3D modelers, thus unable to meet the processing demand for the current explosion of ordinary 3D data. Moreover, their working mechanisms are typically restricted to certain simple topologies, thus relying on cumbersome manual efforts (e.g., surface cutting, part segmentation) for pre-processing. In this paper, we introduce the Flatten Anything Model (FAM), an unsupervised neural architecture to achieve global free-boundary surface parameterization via learning point-wise mappings between 3D points on the target geometric surface and adaptively-deformed UV coordinates within the 2D parameter domain. To mimic the actual physical procedures, we ingeniously construct geometrically-interpretable sub-networks with specific functionalities of surface cutting, UV deforming, unwrapping, and wrapping, which are assembled into a bi-directional cycle mapping framework. Compared with previous methods, our FAM directly operates on discrete surface points without utilizing connectivity information, thus significantly reducing the strict requirements for mesh quality and even applicable to unstructured point cloud data. More importantly, our FAM is fully-automated without the need for pre-cutting and can deal with highly-complex topologies, since its learning process adaptively finds reasonable cutting seams and UV boundaries. Extensive experiments demonstrate the universality, superiority, and inspiring potential of our proposed neural surface parameterization paradigm. Our code is available at https://github.com/keeganhk/FlattenAnything.

Computer Vision

Xingyu Cui, Huanjing Yue, Song Li, Xiangjun Yin, Yusen Hou, Yun Meng, Kai Zou, Xiaolong Hu, Jingyu Yang

Non-line-of-sight (NLOS) imaging allows for seeing hidden scenes around corners through active sensing.Most previous algorithms for NLOS reconstruction require dense transients acquired through regular scans over a large relay surface, which limits their applicability in realistic scenarios with irregular relay surfaces.In this paper, we propose an unsupervised learning-based framework for NLOS imaging from irregularly undersampled transients~(IUT).Our method learns implicit priors from noisy irregularly undersampled transients without requiring paired data, which is difficult and expensive to acquire and align. To overcome the ambiguity of the measurement consistency constraint in inferring the albedo volume, we design a virtual scanning process that enables the network to learn within both range and null spaces for high-quality reconstruction.We devise a physics-guided SURE-based denoiser to enhance robustness to ubiquitous noise in low-photon imaging conditions. Extensive experiments on both simulated and real-world data validate the performance and generalization of our method.Compared with the state-of-the-art (SOTA) method, our method achieves higher fidelity, greater robustness, and remarkably faster inference times by orders of magnitude.The code and model are available at https://github.com/XingyuCuii/Virtual-Scanning-NLOS.

Levi Lingsch, Dana Grund, Siddhartha Mishra, Georgios Kissas

The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator learning surrogates for field prediction while using simulation-based inference (and its variants) for statistical parameter determination. Here, we argue that solving both problems within the same framework can lead to consistent gains in accuracy and robustness. To this end, we propose a novel and flexible formulation of the operator learning problem that jointly predicts continuous quantities and infers distributions of discrete parameters, thereby amortizing the cost of both the inverse and the surrogate models to a joint pre-training step. We present the capabilities of the proposed methodology for predicting continuous and discrete biomarkers in full-body haemodynamics simulations under different levels of missing information. We also consider a test case for atmospheric large-eddy simulation of a two-dimensional dry cold bubble, where we infer both continuous time-series and information about the system's conditions. We present comparisons against different baselines to showcase significantly increased accuracy in both the inverse and the surrogate tasks.

Generative Models

Majdi Hassan, Nikhil Shenoy, Jungyoon Lee, Hannes Stärk, Stephan Thaler, Dominique Beaini

Predicting low-energy molecular conformations given a molecular graph is an important but challenging task in computational drug discovery. Existing state-of-the-art approaches either resort to large scale transformer-based models thatdiffuse over conformer fields, or use computationally expensive methods to gen-erate initial structures and diffuse over torsion angles. In this work, we introduceEquivariant Transformer Flow (ET-Flow). We showcase that a well-designedflow matching approach with equivariance and harmonic prior alleviates the needfor complex internal geometry calculations and large architectures, contrary tothe prevailing methods in the field. Our approach results in a straightforwardand scalable method that directly operates on all-atom coordinates with minimalassumptions. With the advantages of equivariance and flow matching, ET-Flowsignificantly increases the precision and physical validity of the generated con-formers, while being a lighter model and faster at inference. Code is availablehttps://github.com/shenoynikhil/ETFlow.

Computer Vision

Hangcheng Liu, Zhenhu Wu, Hao Wang, Xingshuo Han, Shangwei Guo, Tao Xiang, Tianwei Zhang

Monocular Depth Estimation (MDE) enables the prediction of scene depths from a single RGB image, having been widely integrated into production-grade autonomous driving systems, e.g., Tesla Autopilot. Current adversarial attacks to MDE models focus on attaching an optimized adversarial patch to a designated obstacle. Although effective, this approach presents two inherent limitations: its reliance on specific obstacles and its limited malicious impact. In contrast, we propose a pioneering attack to MDE models that \textit{decouples obstacles from patches physically and deploys optimized patches on roads}, thereby extending the attack scope to arbitrary traffic participants. This approach is inspired by our groundbreaking discovery: \textit{various MDE models with different architectures, trained for autonomous driving, heavily rely on road regions} when predicting depths for different obstacles. Based on this discovery, we design the Adversarial Road Marking (AdvRM) attack, which camouflages patches as ordinary road markings and deploys them on roads, thereby posing a continuous threat within the environment. Experimental results from both dataset simulations and real-world scenarios demonstrate that AdvRM is effective, stealthy, and robust against various MDE models, achieving about 1.507 of Mean Relative Shift Ratio (MRSR) over 8 MDE models. The code is available at \url{https://github.com/a-c-a-c/AdvRM.git}

Datasets and Benchmarks

Hao Zhongkai, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming Liu, Lu Lu 等

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

Language

Zhen Huang, Zengzhi Wang, Shijie Xia, Xuefeng Li, Haoyang Zou, Ruijie Xu, Run-Ze Fan, Lyumanshan Ye, Ethan Chern, Yixin Ye 等

The evolution of Artificial Intelligence (AI) has been significantly accelerated by advancements in Large Language Models (LLMs) and Large Multimodal Models (LMMs), gradually showcasing potential cognitive reasoning abilities in problem-solving and scientific discovery (i.e., AI4Science) once exclusive to human intellect. To comprehensively evaluate current models' performance in cognitive reasoning abilities, we introduce OlympicArena, which includes 11,163 bilingual problems across both text-only and interleaved text-image modalities. These challenges encompass a wide range of disciplines spanning seven fields and 62 international Olympic competitions, rigorously examined for data leakage. We argue that the challenges in Olympic competition problems are ideal for evaluating AI's cognitive reasoning due to their complexity and interdisciplinary nature, which are essential for tackling complex scientific challenges and facilitating discoveries. Beyond evaluating performance across various disciplines using answer-only criteria, we conduct detailed experiments and analyses from multiple perspectives. We delve into the models' cognitive reasoning abilities, their performance across different modalities, and their outcomes in process-level evaluations, which are vital for tasks requiring complex reasoning with lengthy solutions. Our extensive evaluations reveal that even advanced models like GPT-4o only achieve a 39.97\% overall accuracy (28.67\% for mathematics and 29.71\% for physics), illustrating current AI limitations in complex reasoning and multimodal integration. Through the OlympicArena, we aim to advance AI towards superintelligence, equipping it to address more complex challenges in science and beyond. We also provide a comprehensive set of resources to support AI research, including a benchmark dataset, an open-source annotation platform, a detailed evaluation tool, and a leaderboard with automatic submission features.

Physical Models · Physics

Yusong Wang, Chaoran Cheng, Shaoning Li, Yuxuan Ren, Bin Shao, Ge Liu, Pheng-Ann Heng, Nanning Zheng

Geometric graph neural networks (GNNs) have emerged as powerful tools for modeling molecular geometry. However, they encounter limitations in effectively capturing long-range interactions in large molecular systems. To address this challenge, we introduce **Neural P$^3$M**, a versatile enhancer of geometric GNNs to expand the scope of their capabilities by incorporating mesh points alongside atoms and reimaging traditional mathematical operations in a trainable manner. Neural P$^3$M exhibits flexibility across a wide range of molecular systems and demonstrates remarkable accuracy in predicting energies and forces, outperforming on benchmarks such as the MD22 dataset. It also achieves an average improvement of 22% on the OE62 dataset while integrating with various architectures. Codes are available at https://github.com/OnlyLoveKFC/Neural_P3M.

Physical Models

Mingrui Zhang, Chunyang Wang, Stephan C. Kramer, Joseph G Wallwork, Siyi Li, Jiancheng Liu, Xiang Chen, Matthew Piggott

Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method out-performs existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Ampère PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page can be found at https://erizmr.github.io/UM2N/.

Vladimir Malinovskii, Denis Mazur, Ivan Ilin, Denis Kuznedelev, Konstantin Burlachenko, Kai Yi, Dan Alistarh, Peter Richtarik

There has been significant interest in "extreme" compression of large language models (LLMs), i.e. to 1-2 bits per parameter, which allows such models to be executed efficiently on resource-constrained devices. Existing work focused on improved one-shot quantization techniques and weight representations; yet, purely post-training approaches are reaching diminishing returns in terms of the accuracy-vs-bit-width trade-off. State-of-the-art quantization methods such as QuIP# and AQLM include fine-tuning (part of) the compressed parameters over a limited amount of calibration data; however, such fine-tuning techniques over compressed weights often make exclusive use of straight-through estimators (STE), whose performance is not well-understood in this setting. In this work, we question the use of STE for extreme LLM compression, showing that it can be sub-optimal, and perform a systematic study of quantization-aware fine-tuning strategies for LLMs.We propose PV-Tuning - a representation-agnostic framework that generalizes and improves upon existing fine-tuning strategies, and provides convergence guarantees in restricted cases.On the practical side, when used for 1-2 bit vector quantization, PV-Tuning outperforms prior techniques for highly-performant models such as Llama and Mistral. Using PV-Tuning, we achieve the first Pareto-optimal quantization for Llama-2 family models at 2 bits per parameter.

Physical Models

Max Hamilton, Christian Lange, Elijah Cole, Alexander Shepard, Samuel Heinrich, Oisin Mac Aodha, Grant Van Horn, Subhransu Maji

Species range maps (SRMs) are essential tools for research and policy-making in ecology, conservation, and environmental management. However, traditional SRMs rely on the availability of environmental covariates and high-quality observational data, both of which can be challenging to obtain due to geographic inaccessibility and resource constraints. We propose a novel approach combining millions of citizen science species observations with textual descriptions from Wikipedia, covering habitat preferences and range descriptions for tens of thousands of species. Our framework maps location, species, and text descriptions into a common space, facilitating the learning of rich spatial covariates at a global scale and enabling zero-shot range estimation from textual descriptions. Evaluated on held-out species, our zero-shot SRMs significantly outperform baselines and match the performance of SRMs obtained using tens of observations. Our approach also acts as a strong prior when combined with observational data, resulting in more accurate range estimation with less data. We present extensive quantitative and qualitative analyses of the learned representations in the context of range estimation and other spatial tasks, demonstrating the effectiveness of our approach.

Hao Xu, Jia Pan

Machine learning models provide alternatives for efficiently recognizing complex patterns from data, but the main concern in applying them to modeling physical systems stems from their physics-agnostic design, leading to learning methods that lack interpretability, robustness, and data efficiency. This paper mitigates this concern by incorporating the Helmholtz-Hodge decomposition into a Gaussian process model, leading to a versatile framework that simultaneously learns the curl-free and divergence-free components of a dynamical system. Learning a predictive model in this form facilitates the exploitation of symmetry priors. In addition to improving predictive power, these priors make the model indentifiable, thus the identified features can be linked to comprehensible scientific properties of the system. We show that compared to baseline models, our model achieves better predictive performance on several benchmark dynamical systems while allowing physically meaningful decomposition of the systems from noisy and sparse data.

Computer Vision

Guanqi Zhan, Chuanxia Zheng, Weidi Xie, Andrew Zisserman

Our objective in this paper is to probe large vision models to determine to what extent they ‘understand’ different physical properties of the 3D scene depicted in an image. To this end, we make the following contributions: (i) We introduce a general and lightweight protocol to evaluate whether features of an off-the-shelf large vision model encode a number of physical ‘properties’ of the 3D scene, by training discriminative classifiers on the features for these properties. The probes are applied on datasets of real images with annotations for the property. (ii) We apply this protocol to properties covering scene geometry, scene material, support relations, lighting, and view-dependent measures, and large vision models including CLIP, DINOv1, DINOv2, VQGAN, Stable Diffusion. (iii) We find that features from Stable Diffusion and DINOv2 are good for discriminative learning of a number of properties, including scene geometry, support relations, shadows and depth, but less performant for occlusion and material, while outperforming DINOv1, CLIP and VQGAN for all properties. (iv) It is observed that different time steps of Stable Diffusion features, as well as different transformer layers of DINO/CLIP/VQGAN, are good at different properties, unlocking potential applications of 3D physical understanding.

Language · Knowledge

Shuofei Qiao, Runnan Fang, Ningyu Zhang, Yuqi Zhu, Xiang Chen, Shumin Deng, Yong Jiang, Pengjun Xie, Fei Huang, Huajun Chen

Recent endeavors towards directly using large language models (LLMs) as agent models to execute interactive planning tasks have shown commendable results. Despite their achievements, however, they still struggle with brainless trial-and-error in global planning and generating hallucinatory actions in local planning due to their poor understanding of the "real" physical world. Imitating humans' mental world knowledge model which provides global prior knowledge before the task and maintains local dynamic knowledge during the task, in this paper, we introduce parametric World Knowledge Model (WKM) to facilitate agent planning. Concretely, we steer the agent model to self-synthesize knowledge from both expert and sampled trajectories. Then we develop WKM, providing prior task knowledge to guide the global planning and dynamic state knowledge to assist the local planning. Experimental results on three real-world simulated datasets with Mistral-7B, Gemma-7B, and Llama-3-8B demonstrate that our method can achieve superior performance compared to various strong baselines. Besides, we analyze to illustrate that our WKM can effectively alleviate the blind trial-and-error and hallucinatory action issues, providing strong support for the agent's understanding of the world. Other interesting findings include: 1) our instance-level task knowledge can generalize better to unseen tasks, 2) weak WKM can guide strong agent model planning, and 3) unified WKM training has promising potential for further development.

Physical Models · Physics

Louis Serrano, Thomas X Wang, Etienne Le Naour, Jean-Noël Vittaut, Patrick Gallinari

We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors.

Physical Models · Climate

Tung Nguyen, Rohan Shah, Hritik Bansal, Troy Arcomano, Romit Maulik, Rao Kotamarthi, Ian Foster, Sandeep Madireddy, Aditya Grover

Weather forecasting is a fundamental problem for anticipating and mitigating the impacts of climate change. Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success. Here we introduce Stormer, a simple transformer model that achieves state-of-the art performance on weather forecasting with minimal changes to the standard transformer backbone. We identify the key components of Stormer through careful empirical analyses, including weather-specific embedding, randomized dynamics forecast, and pressure-weighted loss. At the core of Stormer is a randomized forecasting objective that trains the model to forecast the weather dynamics over varying time intervals. During inference, this allows us to produce multiple forecasts for a target lead time and combine them to obtain better forecast accuracy. On WeatherBench 2, Stormer performs competitively at short to medium-range forecasts and outperforms current methods beyond 7 days, while requiring orders-of-magnitude less training data and compute. Additionally, we demonstrate Stormer’s favorable scaling properties, showing consistent improvements in forecast accuracy with increases in model size and training tokens. Code and checkpoints are available at https://github.com/tung-nd/stormer.

Jianrui Zhang, Mu Cai, Tengyang Xie, Yong Jae Lee

We propose CounterCurate, a framework to comprehensively improve the visio-linguistic compositional reasoning capability for both contrastive and generative multimodal models. In particular, we identify two critical under- explored problems: the neglect of physically grounded reasoning (counting and position understanding) and the potential of using highly capable text and image generation models for semantic counterfactual fine-tuning. Our work pioneers an approach in addressing these gaps.We first spotlight the near-chance performance of multimodal models like CLIP and LLaVA in physically grounded compositional reasoning. We then apply simple data augmentation using the grounded image generation model GLIGEN to generate fine-tuning data, resulting in significant performance improvements: +33% and +37% for CLIP and LLaVA, respectively, on our newly curated Flickr30k-Positions benchmark. Moreover, we exploit the capabilities of high-performing text generation and image generation models, specifically GPT-4V and DALLE-3, to curate challenging semantic counterfactuals, thereby further enhancing compositional reasoning capabilities on benchmarks such as SugarCrepe, where CounterCurate outperforms GPT-4V.To facilitate future research, we release ourcode, dataset, benchmark, and checkpoints at https://countercurate.github.io/

Nadine Amin, Julia Rayz

While large language and vision-language models showcase impressive capabilities, they face a notable limitation: the inability to connect language with the physical world. To bridge this gap, research has focused on embodied language learning, where the language learner is situated in the world, perceives it, and interacts with it. This article explores the current standing of research in embodied language learning, highlighting opportunities and discussing common challenges. Lastly, it identifies existing gaps from the perspective of language understanding research within the embodied world and suggests potential future directions.

Guiyang Hou, Yongliang Shen, Weiming Lu

Understanding sentiment is arguably an advanced and important capability of AI agents in the physical world. In previous works, many efforts have been devoted to individual sentiment subtasks, without considering interrelated sentiment knowledge among these subtasks. Although some recent works model multiple sentiment subtasks in a unified manner, they merely simply combine these subtasks without deeply exploring the hierarchical relationships among subtasks. In this paper, we introduce GSA-7B, an open-source large language model specific to the sentiment domain. Specifically, we deeply explore the hierarchical relationships between sentiment subtasks, proposing progressive sentiment reasoning benchmark and progressive task instructions. Subsequently, we use Llama2-7B as the backbone model and propose parameter-efficient progressive tuning paradigm which is implemented by constructing chain of LoRA, resulting in the creation of GSA-7B. Experimental results show that GSA-7B as a unified model performs well across all datasets in the progressive sentiment reasoning benchmark. Additionally, under the few-shot setting, GSA-7B also exhibits good generalization ability for sentiment subtasks and datasets that were not encountered during its training phase.