Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling

Learning complex physical dynamics purely from data is challenging due to the intrinsic properties of systems to be satisfied. Incorporating physics-informed priors, such as in Hamiltonian Neural Networks (HNNs), achieves high-precision modeling for energy-conservative systems. However, real-world systems often deviate from strict energy conservation and follow different physical priors. To address this, we present a framework that achieves high-precision modeling for a wide range of dynamical systems from the numerical aspect, by enforcing Time-Reversal Symmetry (TRS) via a novel regularization term. It helps preserve energies for conservative systems while serving as a strong inductive bias for non-conservative, reversible systems. While TRS is a domain-specific physical prior, we present the first theoretical proof that TRS loss can universally improve modeling accuracy by minimizing higher-order Taylor terms in ODE integration, which is numerically beneficial to various systems regardless of their properties, even for irreversible systems. By integrating the TRS loss within neural ordinary differential equation models, the proposed model TREAT demonstrates superior performance on diverse physical systems. It achieves a significant 11.5% MSE improvement in a challenging chaotic triple-pendulum scenario, underscoring TREAT's broad applicability and effectiveness.

DELTA: Dual Consistency Delving with Topological Uncertainty for Active Graph Domain Adaptation

Graph domain adaptation has recently enabled knowledge transfer across different graphs. However, without the semantic information on target graphs, the performance on target graphs is still far from satisfactory. To address the issue, we study the problem of active graph domain adaptation, which selects a small quantitative of informative nodes on the target graph for extra annotation. This problem is highly challenging due to the complicated topological relationships and the distribution discrepancy across graphs. In this paper, we propose a novel approach named Dual Consistency Delving with Topological Uncertainty (DELTA) for active graph domain adaptation. Our DELTA consists of an edge-oriented graph subnetwork and a path-oriented graph subnetwork, which can explore topological semantics from complementary perspectives. In particular, our edge-oriented graph subnetwork utilizes the message passing mechanism to learn neighborhood information, while our path-oriented graph subnetwork explores high-order relationships from substructures. To jointly learn from two subnetworks, we roughly select informative candidate nodes with the consideration of consistency across two subnetworks. Then, we aggregate local semantics from its K-hop subgraph based on node degrees for topological uncertainty estimation. To overcome potential distribution shifts, we compare target nodes and their corresponding source nodes for discrepancy scores as an additional component for fine selection. Extensive experiments on benchmark datasets demonstrate that DELTA outperforms various state-of-the-art approaches.

Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey

This paper explores the recent advancements in enhancing Computational Fluid Dynamics (CFD) tasks through Machine Learning (ML) techniques. We begin by introducing fundamental concepts, traditional methods, and benchmark datasets, then examine the various roles ML plays in improving CFD. The literature systematically reviews papers in recent five years and introduces a novel classification for forward modeling: Data-driven Surrogates, Physics-Informed Surrogates, and ML-assisted Numerical Solutions. Furthermore, we also review the latest ML methods in inverse design and control, offering a novel classification and providing an in-depth discussion. Then we highlight real-world applications of ML for CFD in critical scientific and engineering disciplines, including aerodynamics, combustion, atmosphere & ocean science, biology fluid, plasma, symbolic regression, and reduced order modeling. Besides, we identify key challenges and advocate for future research directions to address these challenges, such as multi-scale representation, physical knowledge encoding, scientific foundation model and automatic scientific discovery. This review serves as a guide for the rapidly expanding ML for CFD community, aiming to inspire insights for future advancements. We draw the conclusion that ML is poised to significantly transform CFD research by enhancing simulation accuracy, reducing computational time, and enabling more complex analyses of fluid dynamics. The paper resources can be viewed at https://github.com/WillDreamer/Awesome-AI4CFD.

TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems

Learning complex multi-agent system dynamics from data is crucial across many domains, such as in physical simulations and material modeling. Extended from purely data-driven approaches, existing physics-informed approaches such as Hamiltonian Neural Network strictly follow energy conservation law to introduce inductive bias, making their learning more sample efficiently. However, many real-world systems do not strictly conserve energy, such as spring systems with frictions. Recognizing this, we turn our attention to a broader physical principle: Time-Reversal Symmetry, which depicts that the dynamics of a system shall remain invariant when traversed back over time. It still helps to preserve energies for conservative systems and in the meanwhile, serves as a strong inductive bias for non-conservative, reversible systems. To inject such inductive bias, in this paper, we propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE). It effectively imposes time-reversal symmetry to enable more accurate model predictions across a wider range of dynamical systems under classical mechanics. In addition, we further provide theoretical analysis to show that our regularization essentially minimizes higher-order Taylor expansion terms during the ODE integration steps, which enables our model to be more noise-tolerant and even applicable to irreversible systems. Experimental results on a variety of physical systems demonstrate the effectiveness of our proposed method. Particularly, it achieves an MSE improvement of 11.5 % on a challenging chaotic triple-pendulum systems.

Bi-Stride Multi-Scale Graph Neural Network for Mesh-Based Physical Simulation

Learning physical systems on unstructured meshes by flat Graph neural networks (GNNs) faces the challenge of modeling the long-range interactions due to the scaling complexity w.r.t. the number of nodes, limiting the generalization under mesh refinement. On regular grids, the convolutional neural networks (CNNs) with a U-net structure can resolve this challenge by efficient stride, pooling, and upsampling operations. Nonetheless, these tools are much less developed for graph neural networks (GNNs), especially when GNNs are employed for learning large-scale mesh-based physics. The challenges arise from the highly irregular meshes and the lack of effective ways to construct the multi-level structure without losing connectivity. Inspired by the bipartite graph determination algorithm, we introduce Bi-Stride Multi-Scale Graph Neural Network (BSMS-GNN) by proposing \textit{bi-stride} as a simple pooling strategy for building the multi-level GNN. \textit{Bi-stride} pools nodes by striding every other BFS frontier; it 1) works robustly on any challenging mesh in the wild, 2) avoids using a mesh generator at coarser levels, 3) avoids the spatial proximity for building coarser levels, and 4) uses non-parametrized aggregating/returning instead of MLPs during pooling and unpooling. Experiments show that our framework significantly outperforms the state-of-the-art method's computational efficiency in representative physics-based simulation cases.