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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
BibTeX:
@inproceedings{schwencke2025anagram,
title={{ANaGRAM}: {A} Natural Gradient Relative to Adapted Model for efficient {PINNs} learning},
author={Schwencke, Nilo and Furtlehner, Cyril},
booktitle={The Thirteenth International Conference on Learning Representations ({ICLR})},
year={2025},
url={https://proceedings.iclr.cc/paper_files/paper/2025/hash/38b445e98823a02479582302ee3aa8e4-Abstract-Conference.html}
}
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, 2025
BibTeX:
@misc{schwencke2025amstramgram,
title={{AMStraMGRAM}: Adaptive Multi-cutoff Strategy Modification for {ANaGRAM}},
author={Schwencke, Nilo and Rousselot, Cyriaque and Shilova, Alena and Furtlehner, Cyril},
year={2025},
eprint={2510.15998},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
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
BibTeX:
@inproceedings{marieanne2025ift,
title={Implicit function theorem in {Physics-Informed Neural Networks} to solve parameterized differential equations},
author={Marie-Anne, Julien and Rousselot, Cyriaque and Schwencke, Nilo and Shilova, Alena},
booktitle={{EurIPS} 2025 Workshop on Differentiable Systems ({DiffSys})},
year={2025},
url={https://openreview.net/forum?id=KjyGLUleWh}
}
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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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.
Kernelizing natural gradient, with applications to PINNs
Published:
Talk given at the ESI workshop on Infinite-dimensional Geometry, presenting a kernel-based perspective on natural gradient methods with applications to Physics-Informed Neural Networks (PINNs).
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).
Geometrical perspectives on Physics-Informed Neural Networks
Published:
Talk given at the Méca–AAC day, presenting geometrical perspectives on the training of Physics-Informed Neural Networks (PINNs).
ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning
Published:
Presentation of ANaGRAM at ICLR 2025. ANaGRAM is a theoretically founded and algorithmically efficient natural gradient method for training Physics-Informed Neural Networks (PINNs), connecting natural gradient descent to the Neural Tangent Kernel and the Green function of the PDE operator.
ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning
Published:
Poster presentation of ANaGRAM at the EDF Numerical Analysis school.
ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning
Published:
Talk presenting ANaGRAM, a theoretically founded and algorithmically efficient natural gradient method for training Physics-Informed Neural Networks (PINNs), at the 12th Biennale of the Société de Mathématiques Appliquées et Industrielles (SMAI).
Unifying PINNs and FEMs through the notion of Natural Neural Tangent Kernel
Published:
Talk presenting joint work with Roland Maier (KIT) on a unifying perspective on Physics-Informed Neural Networks (PINNs) and Finite Element Methods (FEMs) through the notion of Natural Neural Tangent Kernel.
Kernelization of Natural Gradient Methods for Physics Informed Neural Networks
Published:
Presentation of a kernelization framework for natural gradient methods applied to Physics-Informed Neural Networks (PINNs).
Kernelization of Natural Gradient Methods for Physics Informed Neural Networks
Published:
Presentation of a kernelization framework for natural gradient methods applied to Physics-Informed Neural Networks (PINNs).
Kernelization of Natural Gradient Methods for Physics Informed Neural Networks (PINNs) with connections to Galerkin methods
Published:
Presentation of a kernelization framework for natural gradient methods applied to Physics-Informed Neural Networks (PINNs), highlighting connections to Galerkin methods.
Natural gradients and kernel methods for Physics Informed Neural Networks (PINNs)
Published:
PhD defense in Computer Science at Université Paris-Saclay, under the supervision of Cyril Furtlehner (TAU Team, INRIA Saclay – A&O–LISN–Paris-Saclay University–CNRS).
Kernelization of Natural Gradient Methods for Physics Informed Neural Networks (PINNs)
Published:
Presentation of a kernelization framework for natural gradient methods applied to Physics-Informed Neural Networks (PINNs).
Kernelization of Natural Gradient Methods for Physics Informed Neural Networks (PINNs)
Published:
Presentation of a kernelization framework for natural gradient methods applied to Physics-Informed Neural Networks (PINNs).
Kernelization of Natural Gradient Methods for Physics Informed Neural Networks (PINNs)
Published:
Presentation of a kernelization framework for natural gradient methods applied to Physics-Informed Neural Networks (PINNs).
Natural Gradients and Kernel Methods for PINNs
Published:
Talk presenting natural gradient and kernel methods for Physics-Informed Neural Networks (PINNs).
Toward a Unified Framework for PINNs and FEMs: A Petrov–Galerkin perspective through the lens of kernel theory
Published:
Talk presenting joint work with Roland Maier (Institute for Applied and Numerical Mathematics, KIT) on a unified framework connecting Physics-Informed Neural Networks (PINNs) and Finite Element Methods (FEMs) through a Petrov–Galerkin perspective and kernel theory.
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.
Efficient PINNs and Natural Gradients in JAX
Published:
Talk presenting an efficient JAX implementation of natural gradient methods for Physics-Informed Neural Networks (PINNs).
JAX for HPC/AI Hybridization Hackathon
Published:
Advanced participant at the JAX for HPC/AI Hybridization Hackathon, September 7–9, 2026.
Talk at IAS Frontiers Conference on Geometry, Dynamics, and Learning (title TBA)
Published:
Talk at GDL2026, an international conference at the intersection of geometric analysis, dynamical systems, and machine learning.
Talk at STOP 2026: Structured and Large Scale Optimization (title TBA)
Published:
Talk at STOP 2026, a workshop on structured and large scale optimization covering inverse problems, multilevel and stochastic optimization, scientific machine learning, and matrix decomposition.
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.