Molecular dynamics (MD) simulations are crucial for understanding and predicting the behavior of molecular systems in biology and chemistry. Yet, predicting long-term dynamics is still challenging. On one hand, it is hard to employ small-timestep models for long-term prediction, due to substantial rollout errors accumulated at each step, not to mention their extremely high time complexity due to the large number of rollout steps. On the other hand, it is hard to use large-timestep models to achieve high accuracy, due to their inability to capture subtle details of the dynamics. To bridge this dichotomy, we propose DoMiNO , a multi-scale framework that decomposes MD dynamics into several temporal resolutions, each governed by a neural graph ordinary differential equation (GraphODE) and is adaptively fused for final predictions. Concretely, DoMiNO operates through three key components: (1) an E(n)-equivariant graph neural network (EGNN) encoder that initializes latent states from a single observed molecular structure, maintaining SE(3) symmetries throughout; (2) a hierarchy of GraphODEs where each level captures scale-specific dynamics over normalized local time intervals, ranging from slow global motions to fast bond vibrations; and (3) an attention-based fusion module that adaptively combines multi-level predictions and reconstructs SE(3)-equivariant 3D coordinates. This design enables each hierarchical level to specialize in its characteristic timescale while preserving molecular symmetries. During inference, DoMiNO flexibly assembles predictions across different temporal resolutions, providing superior performance over both short-term and long-term dynamics. Empirical results on challenging MD benchmarks demonstrate that DoMiNO achieves significant improvements in prediction accuracy, particularly for molecules with pronounced timescale separation. The method exhibits significantly slower error growth over extended horizons compared to both single-scale baselines and state-of-the-art multi-step approaches. Our implementation is available at https://github.com/FrancoTSolis/DoMiNO-TKDD-Code .

Large Language Models (LLMs) demonstrate promising capabilities in solving scientific problems but often suffer from the issue of hallucination. While integrating LLMs with tools can mitigate this issue, models fine-tuned on tool usage become overreliant on them and incur unnecessary costs. Inspired by how human experts assess problem complexity before selecting solutions, we propose a novel two-component fine-tuning method, Adapting while Learning (AWL). In the first component World Knowledge Learning (WKL), LLMs internalize scientific knowledge by learning from tool-generated solutions. In the second component Tool Usage Adaptation (TUA), we categorize problems as easy or hard based on the model’s accuracy, and train it to maintain direct reasoning for easy problems while switching to tools for hard ones. We validate our method on 6 scientific benchmark datasets across climate science, epidemiology, physics, and other domains. Compared to the original instruct model (8B), models post-trained with AWL achieve 29.11% higher answer accuracy and 12.72% better tool usage accuracy, even surpassing state-of-the-art models including GPT-4o and Claude-3.5 on 4 custom-created datasets. Our code is open-source at https://github.com/Rose-STL-Lab/Adapting-While-Learning.

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.

We introduce a variational formulation for simulating sticky interactions between elastoplastic solids. Our method brings a wider range of material behaviors into the reach of the Incremental Potential Contact (IPC) solver recently developed by (Li et al. 2020). Extending IPC requires several contributions. We first augment IPC with the classical Raous-Cangemi-Cocou (RCC) adhesion model. This allows us to robustly simulate the sticky interactions between arbitrary codimensional-0, 1, and 2 geometries. To enable user-friendly practical adoptions of our method, we further introduce a physically parametrized, easily controllable normal adhesion formulation based on the unsigned distance, which is fully compatible with IPC's barrier formulation. Furthermore, we propose a smoothly clamped tangential adhesion model that naturally models intricate behaviors including debonding. Lastly, we perform benchmark studies comparing our method with the classical models as well as real-world experimental results to demonstrate the efficacy of our method.

Learning the long-range interactions on large-scale mesh-based physical systems with flat Graph Neural Networks (GNNs) and stacking Message Passings (MPs) is challenging due to the scaling complexity w.r.t. the number of nodes and over-smoothing. Therefore, there has been growing interest in the community to introduce multi-scale structures to GNNs for physics simulation. However, current state-of-the-art methods are limited by their reliance on the labor-heavy drawing of coarser meshes or building coarser levels based on spatial proximity, which can introduce wrong edges across geometry boundaries. Inspired by the bipartite graph determination, we propose a novel pooling strategy, bi-stride to tackle the aforementioned limitations. Bi-stride pools nodes on every other frontier of the Breadth-First-Search (BFS), without the need for the manual drawing of coarser meshes and, avoid wrong edges introduced by spatial proximity. Additionally, it enables a reduced number of MP times on each level and the non-parametrized pooling and unpooling by interpolations, similar to convolutional Neural Networks (CNNs), which significantly reduces computational requirements. Experiments show that the proposed framework, BSMS-GNN, significantly outperforms existing methods in terms of both accuracy and computational efficiency in representative physics-based simulation scenarios.

In this paper, we propose a neural network-based approach for learning to represent the behavior of plastic solid materials ranging from rubber and metal to sand and snow. Unlike elastic forces such as spring forces, these plastic forces do not result from the positional gradient of any potential energy, imposing great challenges on the stability and flexibility of their simulation. Our method effectively resolves this issue by learning a generalizable plastic energy whose derivative closely matches the analytical behavior of plastic forces. Our method, for the first time, enables the simulation of a wide range of arbitrary elasticity-plasticity combinations using time step-independent, unconditionally stable optimization-based time integrators. We demonstrate the efficacy of our method by learning and producing challenging 2D and 3D effects of metal, sand, and snow with complex dynamics.

This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured.