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PhD Thesis [PDF]
Symplectic Numerical Integration at the service of Accelerated Optimization and Structure-Preserving Dynamics Learning
Valentin Duruisseaux, 2023.
Physics-Informed Machine Learning
1. Fourier Neural Operators Explained: A Practical Perspective
Valentin Duruisseaux, Jean Kossaifi, Anima Anandkumar, 2025.
Coming soon
2. Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning
Julius Berner, Miguel Liu-Schiaffini, Jean Kossaifi, Valentin Duruisseaux, Boris Bonev, Kamyar Azizzadenesheli, Anima Anandkumar, 2025.
3. A Library for Learning Neural Operators
Jean Kossaifi, Nikola Kovachki, Zongyi Li, David Pitt, Miguel Liu-Schiaffini, Valentin Duruisseaux, Robert J. George, Boris Bonev, Kamyar Azizzadenesheli, Julius Berner, and Anima Anandkumar, 2024.
arxiv.org/abs/2412.10354
4. NOBLE -- Neural Operator with Biologically-informed Latent Embeddings to Capture Experimental Variability in Biological Neuron Models
Luca Ghafourpour, Valentin Duruisseaux, Bahareh Tolooshams, Philip H. Wong, Costas A. Anastassiou, Anima Anandkumar
NeurIPS 2025.
openreview.net/forum?id=CmY6DzEG7Z arxiv.org/abs/2506.04536
5. Enabling Automatic Differentiation with Mollified Graph Neural Operators
Ryan Y. Lin, Julius Berner, Valentin Duruisseaux, David Pitt, Daniel Leibovici, Jean Kossaifi, Kamyar Azizzadenesheli, and Anima Anandkumar.
TMLR 2025.
6. FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation
Adarsh Ganeshram, Haydn Maust, Valentin Duruisseaux, Zongyi Li, Yixuan Wang, Daniel Leibovici, Oscar Bruno, Thomas Hou, Anima Anandkumar, 2025.
7. Fourier Neural Operators for Fast Simulation and Inverse Design of Second-Harmonic Generation in TFLN Waveguide
Valentin Duruisseaux, Robert M. Gray, Siyuan Jiang, Selina Zhou, Robert J. George, Kamyar Azizzadenesheli, Alireza Marandi, Anima Anandkumar
NeurIPS Workshop on Machine Learning and the Physical Sciences, 2025.
Coming soon
8. Inverse Design with Fourier Neural Operators for Quantum System Control
Anastasia Pipi, Nivedha Gopinath, Valentin Duruisseaux, Myrl G. Marmarelis, Taylor L. Patti, Brucek Khailany, Prineha Narang, Anima Anandkumar
NeurIPS Workshop on Machine Learning and the Physical Sciences, 2025.
Coming soon
9. Boundary-Augmented Neural Operators for Better Generalization to Unseen Geometries
Jiayi Zhou, Valentin Duruisseaux, Daniel Z. Huang, Anima Anandkumar
NeurIPS Workshop on AI for Science, 2025.
Coming soon
10. Coarse-to-Fine 3D MRI Reconstruction via 3D Neural Operators
Armeet S. Jatyani, Jiayun Wang, Ryan Y. Lin, Valentin Duruisseaux, Anima Anandkumar
NeurIPS Workshop on Imageomics, 2025.
Coming soon
11. FG-ConvNO: A Geometry-Aware Neural Operator for Propeller CFD Prediction
Yichen Di, Valentin Duruisseaux, Di Zhou, Xinyi Li, Daniel Leibovici, Jean Kossaifi, Anima Anandkumar
AAAI AI2ASE Workshop, 2026.
Coming soon
12. Towards Enforcing Hard Physics Constraints in Operator Learning Frameworks
Valentin Duruisseaux, Miguel Liu-Schiaffini, Julius Berner, and Anima Anandkumar
ICML 2024 AI for Science Workshop
13. Projected Neural Differential Equations for Learning Constrained Dynamics
Alistair White, Anna Büttner, Maximilian Gelbrecht, Valentin Duruisseaux, Niki Kilbertus, Frank Hellmann, and Niklas Boers, 2024.
14. An Operator Learning Framework for Spatiotemporal Super-Resolution of Scientific Simulations
Valentin Duruisseaux, and Amit Chakraborty, 2023.
15. Approximation of Nearly-Periodic Symplectic Maps via Structure-Preserving Neural Networks
Valentin Duruisseaux, Joshua W. Burby, and Qi Tang
Scientific Reports, vol. 13, no. 8351, 2023.
Collection on "Physics-informed Machine Learning and its real-world applications".
doi.org/10.1038/s41598-023-34862-w arxiv.org/abs/2210.05087
Python (TensorFlow) codes are available at github.com/vduruiss/SymplecticGyroceptron
16. Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems
Valentin Duruisseaux, Thai Duong, Melvin Leok, and Nikolay Atanasov
Proceedings of the 5th Learning for Dynamics and Control Conference (L4DC)
PMLR 211:731-744, 2023.
proceedings.mlr.press/v211/duruisseaux23a.html arxiv.org/abs/2211.16006
Python (PyTorch) codes are available at github.com/thaipduong/LieFVIN
Accelerated Optimization via Geometric Numerical Integration
17. Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization
Valentin Duruisseaux, Jeremy Schmitt, and Melvin Leok
SIAM Journal on Scientific Computing, vol. 43, no. 4, A2949–A2980, 2021.
doi.org/10.1137/20M1383835 arxiv.org/abs/1709.01975
18. A Variational Formulation of Accelerated Optimization on Riemannian Manifolds
Valentin Duruisseaux, and Melvin Leok
SIAM Journal on Mathematics of Data Science, vol. 4, no. 2, pages 649-674, 2022.
doi.org/10.1137/21M1395648 arxiv.org/abs/2101.06552
19. Variational Accelerated Optimization on Riemannian Manifolds
Valentin Duruisseaux, and Melvin Leok
IEICE Proceedings Series 71 (B1L-D-03)
International Symposium on Nonlinear Theory and Its Applications (NOLTA), 2022.
doi.org/10.34385/proc.71.B1L-D-03
20. Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators
Valentin Duruisseaux, and Melvin Leok
Journal of Nonlinear Science, vol. 32, no. 42, 2022.
doi.org/10.1007/s00332-022-09795-9 arxiv.org/abs/2104.07176
21. Accelerated Optimization on Riemannian Manifolds via Projected Variational Integrators
Valentin Duruisseaux, and Melvin Leok, 2022.
arxiv.org/abs/2201.02904
22. Time-adaptive Lagrangian Variational Integrators for Accelerated Optimization on Manifolds
Valentin Duruisseaux, and Melvin Leok
Journal of Geometric Mechanics, vol.15, issue 1, pages 224-255, 2023.
doi.org/10.3934/jgm.2023010 arxiv.org/abs/2201.03774
23. Practical Perspectives on Symplectic Accelerated Optimization
Valentin Duruisseaux, and Melvin Leok
Optimization Methods and Software, vol.38, issue 6, pages 1230-1268, 2023.
doi.org/10.1080/10556788.2023.2214837 arxiv.org/abs/2207.11460
Python, MATLAB and Julia codes are available at github.com/vduruiss/AccOpt_via_GNI
Other Topics
Riemannian Optimization
24. Practical Structured Riemannian Optimization with Momentum by using Generalized Normal Coordinates
Wu Lin, Valentin Duruisseaux, Melvin Leok, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt
NeurIPS Workshop on Symmetry and Geometry in Neural Representations, 2022.
openreview.net/forum?id=1aybhSfabqh
Python codes are available at github.com/yorkerlin/StructuredNGD-DL
25. Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning
Wu Lin, Valentin Duruisseaux, Melvin Leok, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt
Proceedings of the 40th International Conference on Machine Learning (ICML)
PMLR 202:21026-21050, 2023.
proceedings.mlr.press/v202/lin23c.html arxiv.org/abs/2302.09738
Python codes are available at github.com/yorkerlin/StructuredNGD-DL
Numerical Bifurcation Analysis of Differential Equations
26. Bistability, Bifurcations and Chaos in the Mackey-Glass Equation
Valentin Duruisseaux, and Antony R. Humphries
Journal of Computational Dynamics, vol. 9, no. 3, pages 421-450, 2022.
doi.org/10.3934/jcd.2022009 arxiv.org/abs/2203.00181
MATLAB codes are available as ancillary files at https://arxiv.org/src/2203.00181v2/anc
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