6 papers
Data-Driven Discovery of Interpretable Kalman Filter Variants through Large Language Models and Genetic Programming
Vasileios Saketos, Sebastian Kaltenbach, Sergey Litvinov +1
Algorithmic discovery has traditionally relied on human ingenuity and extensive experimentation. Here we investigate whether a prominent scientific computing algorithm, the Kalman…
Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data
Lothar Heimbach, Sebastian Kaltenbach, Petr Karnakov +2
Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational…
Optimal Lattice Boltzmann Closures through Multi-Agent Reinforcement Learning
Paul Fischer, Sebastian Kaltenbach, Sergey Litvinov +2
The Lattice Boltzmann method (LBM) offers a powerful and versatile approach to simulating diverse hydrodynamic phenomena, spanning microfluidics to aerodynamics. The vast range of…
Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling
Michal Balcerak, Tamaz Amiranashvili, Antonio Terpin +5
Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate ava…
Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows
Han Gao, Sebastian Kaltenbach, Petros Koumoutsakos
Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-s…
Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observations
Han Gao, Sebastian Kaltenbach, Petros Koumoutsakos
We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial…