Forked Physics Informed Neural Networks for Coupled Systems of Differential equations

• URL: http://arxiv.org/abs/2602.14554v1
• Date: Mon, 16 Feb 2026 08:32:59 GMT
• Title: Forked Physics Informed Neural Networks for Coupled Systems of Differential equations
• Authors: Zhao-Wei Wang, Zhao-Ming Wang,
• Abstract summary: We propose a Forked PINN framework designed for coupled systems of differential equations (DEs)<n>We demonstrate the effectiveness of FPINN in simulating non-Markovian open quantum dynamics governed by coupled DEs.<n>For the spin-boson and XXZ models, FPINN accurately captures non-Markovian features, such as quantum coherence revival and information backflow.
• Score: 1.7158443622461192
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Solving coupled systems of differential equations (DEs) is a central problem across scientific computing. While Physics Informed Neural Networks (PINNs) offer a promising, mesh-free approach, their standard architectures struggle with the multi-objective optimization conflicts and local optima traps inherent in coupled problems. To address the first issue, we propose a Forked PINN (FPINN) framework designed for coupled systems of DEs. FPINN employs a shared base network with independent branches, isolating gradient pathways to stabilize training. We demonstrate the effectiveness of FPINN in simulating non-Markovian open quantum dynamics governed by coupled DEs, where multi-objective conflicts and local optima traps often cause evolutionary stagnation. To overcome this second challenge, we incorporate an evolution regularization loss that guides the model away from trivial solutions and ensures physically meaningful evolution. We demonstrate the effectiveness of FPINN in simulating non-Markovian open quantum dynamics governed by coupled DEs, where multi-objective conflicts and local optima traps often cause evolutionary stagnation. For the spin-boson and XXZ models, FPINN accurately captures hallmark non-Markovian features, such as quantum coherence revival and information backflow, significantly outperforming standard PINNs. The proposed FPINN architecture offers a general and effective framework for solving coupled systems of equations, which arise across a broad spectrum from classical physics to modern artificial intelligence, including applications in multi-body rotational dynamics, multi-asset portfolio optimization, chemical reaction kinetics, and deep representation learning.

Related papers

• Multi-Fidelity Physics-Informed Neural Networks with Bayesian Uncertainty Quantification and Adaptive Residual Learning for Efficient Solution of Parametric Partial Differential Equations [0.0]
  MF-BPINN is a novel multi-fidelity framework for solving partial differential equations.<n>We introduce an adaptive residual network with learnable gating mechanisms.<n>We also develop a rigorous Bayesian framework employing Hamiltonian Monte Carlo.
  arXiv  Detail & Related papers  (2026-02-01T12:01:31Z)
• KITINet: Kinetics Theory Inspired Network Architectures with PDE Simulation Approaches [43.872190335490515]
  This paper introduces KITINet, a novel architecture that reinterprets feature propagation through the lens of non-equilibrium particle dynamics.<n>At its core, we propose a residual module that models update as the evolution of a particle system.<n>This formulation mimics particle collisions and energy exchange, enabling adaptive feature refinement via physics-informed interactions.
  arXiv  Detail & Related papers  (2025-05-23T13:58:29Z)
• Mask-PINNs: Mitigating Internal Covariate Shift in Physics-Informed Neural Networks [1.2667864219315372]
  PINNs have emerged as a powerful framework for solving partial differential equations.<n>We propose Mask-PINNs, a learnable mask function to regulate feature distributions.<n>Our results show consistent improvements in prediction accuracy, convergence stability, and robustness.
  arXiv  Detail & Related papers  (2025-05-09T15:38:52Z)
• Advancing Generalization in PINNs through Latent-Space Representations [71.86401914779019]
  Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs)<n>We propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations.<n>We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations.
  arXiv  Detail & Related papers  (2024-11-28T13:16:20Z)
• Towards Model Discovery Using Domain Decomposition and PINNs [44.99833362998488]
  The study evaluates the performance of two approaches, namely Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs) We find a better performance for the FBPINN approach compared to the vanilla PINN approach, even in cases with data from only a quasi-stationary time domain with few dynamics.
  arXiv  Detail & Related papers  (2024-10-02T14:38:37Z)
• Physics-embedded Fourier Neural Network for Partial Differential Equations [35.41134465442465]
  We introduce Physics-embedded Fourier Neural Networks (PeFNN) with flexible and explainable error. PeFNN is designed to enforce momentum conservation and yields interpretable nonlinear expressions. We demonstrate its outstanding performance for challenging real-world applications such as large-scale flood simulations.
  arXiv  Detail & Related papers  (2024-07-15T18:30:39Z)
• Adversarial Training for Physics-Informed Neural Networks [4.446564162927513]
  We propose an adversarial training strategy for PINNs termed by AT-PINNs. AT-PINNs enhance the robustness of PINNs by fine-tuning the model with adversarial samples. We implement AT-PINNs to the elliptic equation with multi-scale coefficients, Poisson equation with multi-peak solutions, Burgers equation with sharp solutions and the Allen-Cahn equation.
  arXiv  Detail & Related papers  (2023-10-18T08:28:43Z)
• Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equations [64.78260098263489]
  In this work, we assess the ability of physics-informed neural networks (PINNs) to solve increasingly-complex coupled ordinary differential equations (ODEs) We show that PINNs eventually fail to produce correct solutions to these benchmarks as their complexity increases. We identify several reasons why this may be the case, including insufficient network capacity, poor conditioning of the ODEs, and high local curvature, as measured by the Laplacian of the PINN loss.
  arXiv  Detail & Related papers  (2022-10-14T15:01:32Z)
• Mitigating Learning Complexity in Physics and Equality Constrained Artificial Neural Networks [0.9137554315375919]
  Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE) In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective function as soft penalties. Here, we show that this specific way of formulating the objective function is the source of severe limitations in the PINN approach when applied to different kinds of PDEs.
  arXiv  Detail & Related papers  (2022-06-19T04:12:01Z)
• Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture [77.59766598165551]
  Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. Here, we propose Auto-PINN, which employs Neural Architecture Search (NAS) techniques to PINN design. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs.
  arXiv  Detail & Related papers  (2022-05-27T03:24:31Z)
• Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning [89.31889875864599]
  We propose an efficient model-based reinforcement learning algorithm for learning in multi-agent systems. Our main theoretical contributions are the first general regret bounds for model-based reinforcement learning for MFC. We provide a practical parametrization of the core optimization problem.
  arXiv  Detail & Related papers  (2021-07-08T18:01:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.