14 papers
An optimal control approach for neural network architecture adaptation with a posteriori error estimation
C G Krishnanunni, Thomas Scott, Tan Bui-Thanh
This work presents a novel approach for adapting neural network architecture along the depth based on a posteriori error estimation. By formulating neural network training as a con…
Laplace-Fisher Gate Identities for Optimal Matrix-Gated Blended Score Estimation
Alois Duston, Tan Bui-Thanh
Sampling from an unnormalized target density by reversing an Ornstein-Uhlenbeck diffusion requires the score of each noise-perturbed marginal law. Two exact identities are availabl…
Learning Chaotic Dynamics through Second-Order Geometric Supervision
Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh
Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics.…
The AI Research Assistant: Promise, Peril, and a Proof of Concept
Tan Bui-Thanh
Can artificial intelligence truly contribute to creative mathematical research, or does it merely automate routine calculations while introducing risks of error? We provide empiric…
Rendezvous Planning from Sparse Observations of Optimally Controlled Targets
Thomas A. Scott, Lukas Taus, Yen-Hsi Richard Tsai +2
We develop a probabilistic framework for \emph{rendezvous planning}: given sparse, noisy observations of a fast-moving target, plan rendezvous spatiotemporal coordinates for a set…
Generalization Limits of In-Context Operator Networks for Higher-Order Partial Differential Equations
Jamie Mahowald, Tan Bui-Thanh
We investigate the generalization capabilities of In-Context Operator Networks (ICONs), a new class of operator networks that build on the principles of in-context learning, for hi…