Invited Talks

I will discuss two ways to obtain rigorous results from machine learning. The first is to use a more interpretable Neural Network architecture. I will explain Kolmogorov-Arnold Networks and how they can be used in symbolic regression. The second approach is to formulate the problem as a (single-player) game and solve it with Reinforcement Learning. By studying episodic rollouts, each step of the agent towards the solution can be studied and its correctness verified. By studying multiple rollouts, one can try to infer the heuristic learned by the RL agent, which can inform human solution strategies. I will illustrate this in examples, and also touch upon the question about how domain knowledge can inform the data representation and with it the ML algorithm.

Understanding and predicting the behavior of materials under extreme environments—such as high pressure, high temperature, and radiation exposure—is a fundamental challenge with implications for energy, defense, and aerospace applications. Traditional quantum-mechanical simulations provide essential accuracy but are prohibitively expensive for large-scale systems. Machine-learned interatomic potentials (MLIPs) offer a powerful alternative, combining the fidelity of quantum methods with the scalability needed for predictive simulations.

In this talk, I will introduce a unified framework for constructing, training, and deploying MLIPs capable of accurately capturing a wide spectrum of material properties across broad ranges of temperature, pressure, and chemical complexity. The framework is designed to balance physical fidelity, transferability, and computational efficiency, enabling simulations far beyond the limits of empirical potentials. It integrates three key components: (1) multi-element, many-body proper orthogonal descriptors that compactly encode atomic environments and faithfully capture high-order interactions; (2) environment-adaptive ML potentials that dynamically adjust their form to maintain robustness across chemically and structurally diverse states; and (3) a scalable Monte Carlo–driven sampling strategy that ensures broad coverage of equilibrium and nonequilibrium configurations, reducing extrapolation errors without relying on expensive ab-initiomolecular dynamics.

I will demonstrate MLIPs for studying phase transitions, defect dynamics, and failure mechanisms under extreme loading conditions. The emphasis will also be on the interdisciplinary connections between machine learning, computational mathematics, and physics-based modeling, showing how MLIPs can serve as a predictive bridge from quantum mechanics to continuum-scale material behavior.

The cycle of scientific discovery is frequently bottlenecked by the slow, manual creation of software to support computational experiments. To address this, we present an AI system that creates expert-level scientific software whose goal is to maximize a quality metric. The system uses a Large Language Model (LLM) and Tree Search (TS) to systematically improve the quality metric and intelligently navigate the large space of possible solutions. The system achieves expert-level results when it explores and integrates complex research ideas from external sources. The effectiveness of tree search is demonstrated across a wide range of benchmarks. In bioinformatics, it discovered 40 novel methods for single-cell data analysis that outperformed the top human-developed methods on a public leaderboard. In epidemiology, it generated 14 models that outperformed the CDC ensemble and all other individual models for forecasting COVID-19 hospitalizations. Our method also produced state-of-the-art software for geospatial analysis, neural activity prediction in zebrafish, time series forecasting and numerical solution of integrals. By devising and implementing novel solutions to diverse tasks, the system represents a significant step towards accelerating scientific progress.

We show that transition to learning can be affected by combining tasks in small language models. We observe this effect in nested functions on two domains of modular arithmetic and permutation matrices. In math, we find that while learning modular sum is challenging for small models, combining it with modular product or max leads to 2-5x smaller models mastering sum. Similarly, in learning the group action in block diagonal permutation matrices we observe 7x smaller models learn if trained jointly on single block operations. Peering into the models, we find that often joint training leads to better representation of elements: training on sum alone often yields random-looking embedding for numbers, whereas joint training leads to clustering in terms of parity, sorting or other number properties.