mlsanityData to 7 Oct 2026

GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws

arXiv 2410.22193 ↗First posted 29 Oct 2024math.NA cs.LG cs.NAcited by 8

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Abstract (arXiv)

We present GoRINNs: numerical analysis-informed (shallow) neural networks for the solution of inverse problems of non-linear systems of conservation laws. GoRINNs is a hybrid/blended machine learning scheme based on high-resolution Godunov schemes for the solution of the Riemann problem in hyperbolic Partial Differential Equations (PDEs). In contrast to other existing machine learning methods that learn the numerical fluxes or just parameters of conservative Finite Volume methods, relying on deep neural networks (that may lead to poor approximations due to the computational complexity involved in their training), GoRINNs learn the closures of the conservation laws per se based on "intelligently" numerical-assisted shallow neural networks. Due to their structure, in particular, GoRINNs provide explainable, conservative schemes, that solve the inverse problem for hyperbolic PDEs, on the basis of approximate Riemann solvers that satisfy the Rankine-Hugoniot condition. The performance of GoRINNs is assessed via four benchmark problems, namely the Burgers', the Shallow Water, the Lighthill-Whitham-Richards and the Payne-Whitham traffic flow models. The solution profiles of these PDEs exhibit shock waves, rarefactions and/or contact discontinuities at finite times. We demonstrate that GoRINNs provide a very high accuracy both in the smooth and discontinuous regions.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 26 of its 86 references that are in the map. First posted on arXiv 29 Oct 2024.

Builds on

26 of 86 references.

References · 26

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14 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 5.

8 papers.

  1. 2025Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Studycited by 11
  2. 2025Neural Entropy-stable conservative flux form neural networks for learning hyperbolic conservation lawscited by 3
  3. 2025Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learningcited by 2
  4. 2026Parametric Hyperbolic Conservation Laws: A Unified Framework for Conservation, Entropy Stability, and Hyperbolicitycited by 1
  5. 2026RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservationcited by 0
  6. 2026Finite Volume-Informed Neural Network Framework for 2D Shallow Water Equations: Rugged Loss Landscapes and the Importance of Data Guidancecited by 0
  7. 2026Physics-conforming Latent Twinscited by 0
  8. 2026CoFINN: Conservation Flux Informed Neural Networks for Physics Problems Governed by Conservation Lawscited by 0