Tag
Introduces TRIE, an evaluation framework for stochastic PDE surrogates that tests reproduction of invariant measures, trustworthy predictive uncertainty, and efficiency. Benchmarks pointwise-trained neural surrogates, approximate uncertainty methods, and generative models on two SPDEs, finding generative models most consistent.
This paper presents MCO-PDE, a competitive optimization framework that discovers shared partial differential equations from multiple observational datasets by combining neural surrogates, soft-competitive weighting, and genetic algorithms for structure search. It demonstrates high accuracy in recovering canonical equations from limited data and handles complex geometries and real-world experiments.
This paper proposes structure-preserving neural surrogates for partial differential equations that integrate Gaussian process regression to provide tractable uncertainty quantification, enabling real-time simulation with closed-form error estimates.
This paper investigates the role of group-equivariant architectures in neural fluid dynamics surrogates, introducing the AB-GATr model. It finds that equivariance is beneficial when data lacks strong alignment, but can degrade performance on highly aligned datasets.