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Research questionHow can neural operators learn nonequilibrium PDE dynamics while preserving energy conservation and entropy production?Learning nonequilibrium PDE dynamics requires capturing reversible energy-conserving evolution alongside irreversible entropy production. These properties are coupled, so enforcing one independently may produce physically inconsistent dynamics.
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Latest papersRecent research connected to this question, newest first.GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural OperatorsThe source concerns neural operators for the GENERIC/metriplectic structure, including learned energy and entropy functionals and reversible and dissipative operators. Evidence covers 1D and 2D FNOs and DeepONet across four PDEs, including zero-shot resolution changes from 64 to 256; continuous-time structural guarantees are exact, while explicit time stepping introduces small drift.research paper · Sep 2, 2026
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