TM4FF introduces a physics-constrained operator learning framework combining Transformer attention with Mamba state-space models for accurate flow field prediction and denoising.
NewSee LICENSE fileFlow Field PredictionOperator LearningTransformer
This paper reveals the multi-conformal symplectic structure preserved by Hamiltonian PDEs regularized via Brinkman penalization, proving an exact local conservation law under a compatibility condition linking the symplectic matrix and penalization projection.
Proposes the Kuramoto Neural Operator, introducing coupled oscillator dynamics into operator learning to overcome limitations of fixed-basis architectures for physical phenomena governed by local interactions.
See LICENSE fileNeural OperatorPDE SolvingCoupled Oscillator
Proposes a collaborative framework of AI virtual labs under a citation-based influence economy to automate neural operator architecture search and training evaluation.
See LICENSE fileNeural OperatorAI AgentAutomated Scientific Discovery
PRONE introduces a Petrov-Galerkin regression framework Ψ(X)K≈Φ(Y) that unifies DMD, SINDy, Koopman regression, and sparse regression as variants of a single construction for data-driven dynamics learning.
See LICENSE fileOperator LearningPetrov-GalerkinDMD
A systematic survey of operator learning covering the theory, architectures and error analysis of DeepONet, FNO and their variants - the reference entry point to learning infinite-dimensional maps.
arXiv preprint (copyright held by authors)Operator LearningSurveyDeepONet
