Physics-Informed Tree Search for High-Dimensional Computational Design

2026-01-10

arXiv.org

AI Summary

This work proposes Physics-Informed Monte Carlo Tree Search (PI-MCTS), a novel approach for high-dimensional, expensive, non-convex black-box optimization problems with physical constraints and no available gradients. PI-MCTS extends the discrete MCTS framework to continuous scientific optimization by integrating physical priors with reinforcement learning principles. The method employs a policy-driven decision tree, surrogate-guided directional sampling, reward shaping, and a hierarchical exploration–exploitation mechanism to efficiently search for optimal solutions while preserving physical consistency. Evaluated on standard benchmark functions and real-world applications—including crystal structure optimization, interatomic potential fitting, and engineering design—PI-MCTS consistently matches or significantly outperforms existing global optimizers, offering strong interpretability, scalability, and solution fidelity.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• high-dimensional optimization
• physics-informed design
• black-box optimization
• computational design
• constrained optimization

Innovation

• Physics-Informed Optimization
• Monte Carlo Tree Search
• High-Dimensional Design
• Surrogate-Guided Sampling
• Scientific Machine Learning