Nilo Schwencke

Nilo Schwencke

Postdoc @ LIP, ENS Lyon on PINNs & SciML

Posts by Collection

portfolio

publications

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.

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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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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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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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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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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talks

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

Published:

Presentation of ANaGRAM, a theoretically founded and algorithmically efficient natural gradient method for training Physics-Informed Neural Networks (PINNs). The talk covers the functional analysis perspective on PINNs training, the connection to the Neural Tangent Kernel, and an efficient SVD-based implementation that reduces the complexity of natural gradient descent significantly.

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

Published:

Presentation of ANaGRAM, a theoretically founded and algorithmically efficient natural gradient method for training Physics-Informed Neural Networks (PINNs). The talk covers the functional analysis perspective on PINNs training, the connection to the Neural Tangent Kernel, and an efficient SVD-based implementation that reduces the complexity of natural gradient descent significantly.

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

Published:

Presentation of ANaGRAM, a theoretically founded and algorithmically efficient natural gradient method for training Physics-Informed Neural Networks (PINNs). The talk covers the functional analysis perspective on PINNs training, the connection to the Neural Tangent Kernel, and an efficient SVD-based implementation that reduces the complexity of natural gradient descent significantly.

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

Published:

Presentation of ANaGRAM, a theoretically founded and algorithmically efficient natural gradient method for training Physics-Informed Neural Networks (PINNs). The talk covers the functional analysis perspective on PINNs training, the connection to the Neural Tangent Kernel, and an efficient SVD-based implementation that reduces the complexity of natural gradient descent significantly.

Addressing Spectral Bias in PINNs

Published:

Talk given at the kick-off meeting of the SCALP project, presenting work on addressing spectral bias in Physics-Informed Neural Networks (PINNs).

Adaptive Sampling in PINNs through the lens of Kernel Theory

Published:

Talk presenting joint work with Sheng Wan, Cyriaque Rousselot, Shorouk El-Hassanieh, Alena Shilova, and Cyril Furtlehner on adaptive sampling strategies for Physics-Informed Neural Networks (PINNs) through the lens of kernel theory.

teaching

Mathematics Oral Examiner (Khôlleur)

Preparatory Class for Engineering Schools (MPSI level), Lycée Blaise Pascal, 2016

Preparation for the oral examinations that form part of the highly competitive entrance process to the French Grandes Écoles. Subjects covered during the first year included:

  • Linear Algebra
  • Elementary General Algebra
  • Real Analysis
  • Ordinary Differential Equations (introductory level)
  • Euclidean Geometry
  • Probability Theory

Teaching Assistant

First-Year Linear Algebra, Karlsruhe Institute of Technology (KIT), Department of Mathematics, 2019

Year-long course covering elementary Linear and Multilinear Algebra, Euclidean Rings, and selected topics in advanced algebra (including Category Theory). Class taught in German, partly online during the COVID period.

Teaching Assistant

Introduction to Python, IUT d’Orsay, Université Paris-Saclay, 2021

Taught practical sessions introducing students to the basics of Python programming and algorithmic thinking. Class taught online due to the COVID period.

Teaching Assistant

Deep Learning (Master MVA), CentraleSupélec, 2021

Taught practical sessions for the Deep Learning in practice course of the Master MVA program. Class taught online due to the COVID period.

Teaching Assistant

Introduction to Algorithms and Graphical Programming (Undergraduate, Year 2), Université Paris-Saclay, 2023

Taught tutorials and practical sessions for second-year undergraduate students, introducing fundamental concepts in algorithms and graphical programming.