Consider a parametric ODE control model. A function of the states and parameters is called observable if its value can in principle be reconstructed from input-output data. The observable functions form a field, called the observation field, represented naturally by a set of generators. Even when the model is not fully...
Alexander Demin, Gleb Pogudin, Christopher Rackauckas· 1 citation
This work exploits the structure that sample-wise batching and local PDE couplings induce in the projection subproblems, exposing this structure using ExaModels.jl and GPU sparse factorization to show that sparse GPU nonlinear optimization is a practical foundation for constrained generative sampling in scientific mach...
Alaina Kolli, Theodoros G. Xenakis, Utkarsh Utkarsh et al.· arXiv.org· 0 citations
This work introduces RLVP: Reinforcement Learning with Verifiable Physics, an RL post-training framework for multi-PDE solver code generation and shows that a smaller LLM post-trained with RLVP can outperform prompting a frontier model on in-distribution PDE solver generation.
Pengfei Cai, Utkarsh Utkarsh, Alan Edelman et al.· arXiv.org· 0 citations
PEM-UDE, a method that combines prediction-error methodology with universal differential equations to discover governing equations from limited, noise-corrupted observations, yields a multi-scale neural mass model that ties single-neuron parameters to macroscopic network dynamics and predicts a relationship between con...
Anthony G. Chesebro, David Hofmann, V. Dixit et al.· 1 citation
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