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Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains
Shizheng Wen, Arsh Kumbhat, Levi Lingsch +4
The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. D…
Neuro-Symbolic AI for Analytical Solutions of Differential Equations
Orestis Oikonomou, Levi Lingsch, Dana Grund +2
Analytical solutions to differential equations offer exact, interpretable insight but are rarely available because discovering them requires expert intuition or exhaustive search o…
RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains
Sepehr Mousavi, Shizheng Wen, Levi Lingsch +3
Learning the solution operators of PDEs on arbitrary domains is challenging due to the diversity of possible domain shapes, in addition to the often intricate underlying physics. W…
FUSE: Fast Unified Simulation and Estimation for PDEs
Levi E. Lingsch, Dana Grund, Siddhartha Mishra +1
The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto…