While complex simulations of physical systems have been widely used in
engineering and scientific computing, lowering their often prohibitive
computational requirements has only recently been tackled by deep learning
approaches. In this paper, we present GraphSplineNets, a novel deep-learning
method to speed up the forecasting of physical systems by reducing the grid
size and number of iteration steps of deep surrogate models. Our method uses
two differentiable orthogonal spline collocation methods to efficiently predict
response at any location in time and space. Additionally, we introduce an
adaptive collocation strategy in space to prioritize sampling from the most
important regions. GraphSplineNets improve the accuracy-speedup tradeoff in
forecasting various dynamical systems with increasing complexity, including the
heat equation, damped wave propagation, Navier-Stokes equations, and real-world
ocean currents in both regular and irregular domains.

提出 GraphSplineNets 深度学习方法，在物理系统的预测中通过减少深度替代模型的网格大小和迭代步骤数来提高计算效率和准确性，包括研究热方程、阻尼波传播、纳维 - 斯托克斯方程和现实世界中规则和不规则域的海流。

使用图形样条网络学习高效的代理动态模型

Learning Efficient Surrogate Dynamic Models with Graph Spline Networks

Adaptive Mesh Refinement (AMR) is crucial for mesh-based simulations, as it
allows for dynamically adjusting the resolution of a mesh to trade off
computational cost with the simulation accuracy. Yet, existing methods for AMR
either use task-dependent heuristics, expensive error estimators, or do not
scale well to larger meshes or more complex problems. In this paper, we
formalize AMR as a Swarm Reinforcement Learning problem, viewing each element
of a mesh as part of a collaborative system of simple and homogeneous agents.
We combine this problem formulation with a novel agent-wise reward function and
Graph Neural Networks, allowing us to learn reliable and scalable refinement
strategies on arbitrary systems of equations. We experimentally demonstrate the
effectiveness of our approach in improving the accuracy and efficiency of
complex simulations. Our results show that we outperform learned baselines and
achieve a refinement quality that is on par with a traditional error-based AMR
refinement strategy without requiring error indicators during inference.

使用 Swarm 强化学习及 Graph 神经网络，将自适应网格细化问题形式化为协作系统，优于传统基于误差的方法，可在复杂模拟中提高准确性和效率。

自适应网格细化的 Swarm 强化学习

Swarm Reinforcement Learning For Adaptive Mesh Refinement

Many domains of science have developed complex simulations to describe
phenomena of interest. While these simulations provide high-fidelity models,
they are poorly suited for inference and lead to challenging inverse problems.
We review the rapidly developing field of simulation-based inference and
identify the forces giving new momentum to the field. Finally, we describe how
the frontier is expanding so that a broad audience can appreciate the profound
change these developments may have on science.

本文旨在回顾模拟推断的最新进展，探讨其在科学领域中的重要性，特别是在高确定性建模方面，以及其拓展如何让更广泛的受众理解其对科学的深远影响。