Adjoint PINN surrogates are constructed to evolve runaway electron fluid moments and distributions for arbitrary initial conditions, achieving orders-of-magnitude speedup over conventional RE solvers with reported validation agreement.
Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
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abstract
We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions and contains no adjustable parameters. The second part is constructed so as not to affect the boundary conditions. This part involves a feedforward neural network, containing adjustable parameters (the weights). Hence by construction the boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ODE's, to systems of coupled ODE's and also to PDE's. In this article we illustrate the method by solving a variety of model problems and present comparisons with finite elements for several cases of partial differential equations.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
A DNN solves the symmetrized spectator form of the subtracted Faddeev equations for three identical bosons, reproducing Efimov binding scales at unitarity to within 0.022% and tracing bound-state branches versus inverse scattering length.
Physics-informed neural networks solve two-flavor neutrino oscillation equations in vacuum and matter with mean squared errors of order 10^{-3} to 10^{-4}, matching analytical results.
citing papers explorer
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Hierarchical Framework of Runaway Electrons using Deep Learning
Adjoint PINN surrogates are constructed to evolve runaway electron fluid moments and distributions for arbitrary initial conditions, achieving orders-of-magnitude speedup over conventional RE solvers with reported validation agreement.
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Neural-network solution of subtracted three-body Faddeev integral equations near the Efimov limit
A DNN solves the symmetrized spectator form of the subtracted Faddeev equations for three identical bosons, reproducing Efimov binding scales at unitarity to within 0.022% and tracing bound-state branches versus inverse scattering length.
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Physics-Informed Neural Networks for Solving Two-Flavor Neutrino Oscillations in Vacuum and Matter Environments for Atmospheric and Reactor Neutrinos
Physics-informed neural networks solve two-flavor neutrino oscillation equations in vacuum and matter with mean squared errors of order 10^{-3} to 10^{-4}, matching analytical results.