Related papers: Symbolic Physics Learner: Discovering governing eq…

The discovery of patterns that accurately discriminate one class label from another remains a challenging data mining task. Subgroup discovery (SD) is one of the frameworks that enables to elicit such interesting hypotheses from labeled…

A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations…

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…

Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of…

Reinforcement Learning (RL) traditionally relies on scalar reward signals, limiting its ability to leverage the rich semantic knowledge often available in real-world tasks. In contrast, humans learn efficiently by combining numerical…

Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…

Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

Learning to control unknown nonlinear dynamical systems is a fundamental problem in reinforcement learning and control theory. A commonly applied approach is to first explore the environment (exploration), learn an accurate model of it…

Based on the existing pivot rules, the simplex method for linear programming is not polynomial in the worst case. Therefore the optimal pivot of the simplex method is crucial. This study proposes the optimal rule to find all shortest pivot…

We draw on the latest advancements in the physics community to propose a novel method for discovering the governing non-linear dynamics of physical systems in reinforcement learning (RL). We establish that this method is capable of…

This paper proposes a novel learning architecture for acquiring generalizable high-level symbolic skills from a few unlabeled low-level skill trajectory demonstrations. The architecture involves neural networks for symbol discovery and…

Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space…

We demonstrate the use of symbolic regression in deriving analytical formulas, which are needed at various stages of a typical experimental analysis in collider phenomenology. As a first application, we consider kinematic variables like the…

Discovering novel catalysts requires complex reasoning involving multiple chemical properties and resultant trade-offs, leading to a combinatorial growth in the search space. While large language models (LLM) have demonstrated novel…

Linear Temporal Logic (LTL) is widely used to specify high-level objectives for system policies, and it is highly desirable for autonomous systems to learn the optimal policy with respect to such specifications. However, learning the…

Visualization of Machine Learning (ML) models is an important part of the ML process to enhance the interpretability and prediction accuracy of the ML models. This paper proposes a new method SPC-DT to visualize the Decision Tree (DT) as…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…

Inference-time scaling strategies, particularly Monte Carlo Tree Search (MCTS), have significantly enhanced the reasoning capabilities of Large Language Models (LLMs). However, current approaches remain predominantly stateless, discarding…