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abstract indexed · arXiv 2610.21049 · updated 2026-10-18

SALTO: Solver-Anchored Lifted Transfer Operators for Nonlinear Event Inference

First page of SALTO: Solver-Anchored Lifted Transfer Operators for Nonlinear Event Inference
From the original paper · arXiv 2610.21049Page 1. Select the image to read the PDF.

SALTO replaces repeated forward/adjoint solves through a numerical PDE simulator for finite-amplitude source inversion with a single trained Koopman model whose lifted transpose propagates sensors backward in one solve and answers candidate events with an encoder pass and an inner product. The cost is an offline training stage plus three structural constraints (anchoring to the simulator's linearized propagator, centered observables, block-triangular propagator), which require access to the simulator's tangent linearization and observable training data. It can fail when events are far outside the training amplitude or location distribution, when no differentiable simulator or its linearization is available, and its accuracy guarantees hold only in the vanishing-amplitude limit rather than for arbitrary perturbations.

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Lifted Koopman adjoints for finite-amplitude source inversion
published
2026-10-15

The method targets PDE inverse problems with an available simulator and its linearized propagator, a workload outside typical LLM/ML production practice, and the claimed gains are validated only on three nonlinear PDE benchmarks, so adoption is premature without a matching scientific-inference workload.

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    SALTO replaces repeated forward/adjoint solves through a numerical PDE simulator for finite-amplitude source inversion with a single trained Koopman model whose lifted transpose propagates sensors backward in one solve and answers candidate events with an encoder pass and an inner product. The cost is an offline training stage plus three structural constraints (anchoring to the simulator's linearized propagator, centered observables, block-triangular propagator), which require access to the simulator's tangent linearization and observable training data. It can fail when events are far outside the training amplitude or location distribution, when no differentiable simulator or its linearization is available, and its accuracy guarantees hold only in the vanishing-amplitude limit rather than for arbitrary perturbations.

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  2. claim 02Paperraft inference

    Posterior sampling for two interacting sources on a reaction-diffusion system at one-twentieth of the solver's cost, with measurement prediction error of 2-8% versus 41-165% for the classical adjoint.

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