Physics-Informed Tree Search for High-Dimensional Computational Design

TL;DR

This paper introduces a physics-informed Monte Carlo Tree Search framework for efficient high-dimensional scientific optimization, integrating physical knowledge to improve exploration and convergence in complex design spaces.

Contribution

The paper presents a novel physics-informed tree search method that combines reinforcement learning concepts with physical modeling for high-dimensional optimization tasks.

Findings

Outperforms standard global optimizers on benchmark functions.

Successfully applied to crystal structure and potential fitting tasks.

Achieves high-fidelity convergence with evaluation efficiency.

Abstract

High-dimensional design spaces underpin a wide range of physics-based modeling and computational design tasks in science and engineering. These problems are commonly formulated as constrained black-box searches over rugged objective landscapes, where function evaluations are expensive, and gradients are unavailable or unreliable. Conventional global search engines and optimizers struggle in such settings due to the exponential scaling of design spaces, the presence of multiple local basins, and the absence of physical guidance in sampling. We present a physics-informed Monte Carlo Tree Search (MCTS) framework that extends policy-driven tree-based reinforcement concepts to continuous, high-dimensional scientific optimization. Our method integrates population-level decision trees with surrogate-guided directional sampling, reward shaping, and hierarchical switching between global exploration and local exploitation. These ingredients allow efficient traversal of non-convex, multimodal landscapes where physically meaningful optima are sparse. We benchmark our approach against standard global optimization baselines on a suite of canonical test functions, demonstrating superior or comparable performance in terms of convergence, robustness, and generalization. Beyond synthetic tests, we demonstrate physics-consistent applicability to (i) crystal structure optimization from clusters to bulk, (ii) fitting of classical interatomic potentials, and (iii) constrained engineering design problems. Across all cases, the method converges with high fidelity and evaluation efficiency while preserving physical constraints. Overall, our work establishes physics-informed tree search as a scalable and interpretable paradigm for computational design and high-dimensional scientific optimization, bridging discrete decision-making frameworks with continuous search in scientific design workflows.