Presentation Information
[U02-P09]Multi-Input Operator Learning for Multiscale Geophysical PDE Systems: A Quantum-Compatible Orthogonal Framework
*Yeyu Zhang1, Kailin Liang1 (1.Shanghai University of Finance and Economics)
Keywords:
Multi-input operator learning,Multiscale geophysical transport,Quantum-compatible neural operators
Multiscale transport and nonlinear dynamics are common in geophysical systems, where the evolution of a state variable depends on multiple functional inputs such as spatially varying coefficients, forcing terms, and initial conditions. Constructing surrogate operators for these systems is nontrivial due to nonlinear coupling and variability across spatial and temporal scales.
We study multi-input operator learning for canonical PDE models relevant to geophysical transport, including advection–diffusion equations, viscous Burgers-type systems, and nonlinear diffusion–reaction dynamics. The proposed framework follows a branch–trunk architecture in which different input functions are encoded separately and then combined in a shared latent representation. To improve numerical stability across network depth, we introduce an orthogonal flow mechanism that restricts linear transformations to be norm-preserving while retaining nonlinear mixing between layers. Numerical experiments with stochastic inputs generated from Gaussian random fields show consistent approximation accuracy and stable performance under spatially varying and nonlinear regimes.
The linear components of the network are constructed from orthogonal transformations whose structure admits a quantum-compatible implementation. The model is trained classically, and the learned parameters can be transferred layer-wise to structured quantum circuits for quantum-simulated forward evaluation, where the outputs agree with classical predictions up to numerical precision. Although demonstrated on canonical operator-learning benchmarks, the framework is intended for surrogate modeling of multiscale transport systems and offers a structured basis for future hybrid classical–quantum operator computation.
We study multi-input operator learning for canonical PDE models relevant to geophysical transport, including advection–diffusion equations, viscous Burgers-type systems, and nonlinear diffusion–reaction dynamics. The proposed framework follows a branch–trunk architecture in which different input functions are encoded separately and then combined in a shared latent representation. To improve numerical stability across network depth, we introduce an orthogonal flow mechanism that restricts linear transformations to be norm-preserving while retaining nonlinear mixing between layers. Numerical experiments with stochastic inputs generated from Gaussian random fields show consistent approximation accuracy and stable performance under spatially varying and nonlinear regimes.
The linear components of the network are constructed from orthogonal transformations whose structure admits a quantum-compatible implementation. The model is trained classically, and the learned parameters can be transferred layer-wise to structured quantum circuits for quantum-simulated forward evaluation, where the outputs agree with classical predictions up to numerical precision. Although demonstrated on canonical operator-learning benchmarks, the framework is intended for surrogate modeling of multiscale transport systems and offers a structured basis for future hybrid classical–quantum operator computation.