A linear estimator for the Schrödinger evolution operator is introduced that enforces weak unitarity, supplies uniform prediction error bounds and time-extrapolation bounds, and reports up to 100x lower relative error than FNO and DeepONet on hydrogen, ion-trap, and optical-lattice Hamiltonians.
To see why, observe that we can rewrite ⟨Λs(∆ψ),Λsψ⟩=⟨(Λs∆Λ −s)Λsψ,Λsψ⟩
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Operator Learning for Schr\"{o}dinger Equation: Unitarity, Error Bounds, and Time Generalization
A linear estimator for the Schrödinger evolution operator is introduced that enforces weak unitarity, supplies uniform prediction error bounds and time-extrapolation bounds, and reports up to 100x lower relative error than FNO and DeepONet on hydrogen, ion-trap, and optical-lattice Hamiltonians.