Publications

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International Conference Papers

ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning

Published in The Thirteenth International Conference on Learning Representations (ICLR 2025), 2025

We introduce ANaGRAM, a natural-gradient method for efficient training of physics-informed neural networks. By exploiting the geometry of the neural model manifold, it provides a scalable optimization scheme together with a principled reformulation of PINNs connected to Green’s function theory.

Recommended citation: Nilo Schwencke, Cyril Furtlehner, "ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning." ICLR, 2025.
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Preprints

Beyond PINNs: A Unified Gauss–Newton and Petrov–Galerkin Framework for Neural and Hybrid PDE Solvers

Published in arXiv preprint, 2026

We introduce a unified Gauss–Newton and Petrov–Galerkin framework for neural and finite element PDE solvers. This leads both to a Gauss–Newton approach to weak formulations of PINNs and to a hybrid finite element–neural strategy acting on complementary approximation spaces.

Recommended citation: Nilo Schwencke, Roland Maier, "Beyond PINNs: A Unified Gauss–Newton and Petrov–Galerkin Framework for Neural and Hybrid PDE Solvers." arXiv preprint arXiv:2609.20641, 2026.
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AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM

Published in arXiv preprint, 2025

We analyze the training dynamics of ANaGRAM and introduce AMStraMGRAM, an adaptive multi-cutoff strategy for its regularization. A spectral perspective explains the role of regularization and leads to substantial accuracy improvements, reaching machine precision on several benchmark PDEs.

Recommended citation: Nilo Schwencke, Cyriaque Rousselot, Alena Shilova, Cyril Furtlehner, "AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM." arXiv, 2025.
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Workshop Papers

Implicit function theorem in Physics-Informed Neural Networks to solve parameterized differential equations

Published in EurIPS 2025 Workshop DiffSys, 2025

We introduce a curriculum-learning strategy for PINNs solving parameterized differential equations. Using an extension of the implicit function theorem, the method follows the solution manifold from an easy problem to a difficult target and connects naturally to natural-gradient optimization.

Recommended citation: Julien Marie-Anne, Cyriaque Rousselot, Nilo Schwencke, Alena Shilova, "Implicit function theorem in Physics-Informed Neural Networks to solve parameterized differential equations." EurIPS 2025 Workshop DiffSys, 2025.
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Theses

Natural gradients and kernel methods for Physics Informed Neural Networks (PINNs)

Published in Université Paris-Saclay, 2025

This dissertation addresses limitations in Physics-Informed Neural Networks (PINNs) through two complementary approaches. Algorithmically, it develops improved training schemes combining kernel methods and natural gradients. Theoretically, it grounds PINNs in rigorous mathematics using Reproducing Kernel Hilbert Spaces (RKHS) and spectral analysis.

Recommended citation: Nilo Schwencke, "Natural gradients and kernel methods for Physics Informed Neural Networks (PINNs)." PhD thesis, Université Paris-Saclay, 2025.
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Simulation of lithium ions batteries using physics informed neural networks

Published in Karlsruhe Institute of Technology (KIT), 2023

Master thesis applying Physics-Informed Neural Networks (PINNs) to the simulation of lithium-ion batteries, with a focus on the underlying PDEs governing electrochemical dynamics.

Recommended citation: Nilo Schwencke, "Simulation of lithium ions batteries using physics informed neural networks." Master thesis, Karlsruhe Institute of Technology (KIT), 2023.