Hybrid model- and data-driven neural operators for acoustic inverse problems
Organization:
Funded by: | ZonMW & PA-Imagng
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PostDoc: |
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Supervisors: | chair MIA:
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Collaboration: | PA-Imaging |
Description:
Neural networks, the backbone of artificial intelligence, has recently been increasingly used for scientific problems. Particularly, it is has been applied to solving inverse problems in medicine and geophysics. Another recent advancement is the neural operator. These neural networks are able to map functions to functions and are mainly used in scientific computing as fast surrogate models for solving complex PDEs.
In inverse problems involving partial differential equations (PDEs), these neural operators can be very important as they are much quicker in solving the PDEs and hence can help in solving the inverse problem faster. One issue, however, is that the neural operators are mainly data-driven. Hence, there are no guarantees that the PDE is solved accurately. This is in contrast when solving the PDE via (slower) model-driven numerical methods. The lack of guarantees is a big issue of the neural operators as inaccurate PDE solutions can have significant negative impact on the obtained solution.
This project tries to tackle this problem for inverse problems in (photo)acoustics. Particularly, we want to combine the model-driven approach with the data-driven neural operators. The goal is to develop a general method that provides improved and faster reconstructions to the inverse problem by using neural operators but that has some additional guarantees by incorporating model-driven components, hence creating a hybrid model.
Output:
Jump to: 2025 | 2024 | 2023 | 2022
Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators (2025)[Working paper › Preprint]. ArXiv.org. Dummer, S., Heeringa, T. J. & Iglesias, J. A.https://doi.org/10.48550/arXiv.2509.26371RONOM: Reduced-Order Neural Operator Modeling (2025)[Working paper › Preprint]. ArXiv.org. Dummer, S., Ye, D. & Brune, C.https://doi.org/10.48550/arXiv.2507.12814Joint Manifold Learning and Optimal Transport for Dynamic Imaging (2025)[Working paper › Preprint]. ArXiv.org. Dummer, S., Vaish, P. & Brune, C.https://doi.org/10.48550/arXiv.2505.11913Joint Manifold Learning and Optimal Transport for Dynamic Imaging (2025)In Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings (pp. 400-411) (Lecture Notes in Computer Science; Vol. 15667 LNCS). Springer. Dummer, S., Vaish, P. & Brune, C.https://doi.org/10.1007/978-3-031-92366-1_31 RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations (2024)SIAM journal on imaging sciences, 17(4), 2302 - 2330. Dummer, S., Brune, C. & Strisciuglio, N.https://doi.org/10.1137/24M1644730Neural Fields for Continuous Periodic Motion Estimation in 4D Cardiovascular Imaging (2024)[Working paper › Preprint]. ArXiv.org. Garzia, S., Rygiel, P., Dummer, S., Cademartiri, F., Celi, S. & Wolterink, J. M.https://doi.org/10.48550/arXiv.2407.20728Rda-Inr: Riemannian Diffeomorphic Autoencoding Via Implicit Neural Representations (2024)[Contribution to conference › Poster] SIAM Conference on Imaging Science, IS 2024. Dummer, S., Strisciuglio, N. & Brune, C.Generative modeling of living cells with SO(3)-equivariant implicit neural representations (2024)Medical image analysis, 91. Article 102991. Wiesner, D., Suk, J., Dummer, S., Nečasová, T., Ulman, V., Svoboda, D. & Wolterink, J. M.https://doi.org/10.1016/j.media.2023.102991 Discovering efficient periodic behaviors in mechanical systems via neural approximators (2023)Optimal Control Applications and Methods, 44(6), 3052-3079. Wotte, Y. P., Dummer, S., Botteghi, N., Brune, C., Stramigioli, S. & Califano, F.https://doi.org/10.1002/oca.3025Riemannian Shape Manifold Learning with Applications to Biological Data (2023)[Contribution to conference › Poster] EEMCS Research Networking Day 2023. Dummer, S., Strisciuglio, N. & Brune, C.Defocus Blur Synthesis and Deblurring via Interpolation and Extrapolation in Latent Space (2023)[Working paper › Preprint]. ArXiv.org. Mazilu, I., Wang, S., Dummer, S., Veldhuis, R., Brune, C. & Strisciuglio, N.https://doi.org/10.48550/arXiv.2307.15461Rda-inr: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations (2023)[Working paper › Preprint]. ArXiv.org. Dummer, S., Strisciuglio, N. & Brune, C.https://doi.org/10.48550/arXiv.2305.12854Generative modeling of living cells with SO(3)-equivariant implicit neural representations (2023)[Working paper › Preprint]. ArXiv.org. Wiesner, D., Suk, J., Dummer, S., Nečasová, T., Ulman, V., Svoboda, D. & Wolterink, J. M.https://doi.org/10.48550/arXiv.2304.08960Defocus Blur Synthesis and Deblurring via Interpolation and Extrapolation in Latent Space (2023)In Computer Analysis of Images and Patterns: 20th International Conference, CAIP 2023, Limassol, Cyprus, September 25–28, 2023, Proceedings (pp. 201-211) (Lecture Notes in Computer Science; Vol. 14185). Springer. Mazilu, I., Wang, S., Dummer, S., Veldhuis, R., Brune, C. & Strisciuglio, N.https://doi.org/10.1007/978-3-031-44240-7_20 Discovering Efficient Periodic Behaviours in Mechanical Systems via Neural Approximators (2022)[Working paper › Preprint]. ArXiv.org. Wotte, Y., Dummer, S., Botteghi, N., Brune, C., Stramigioli, S. & Califano, F.https://doi.org/10.48550/arXiv.2212.14253Structure preserving implicit shape encoding via flow regularization (2022)[Contribution to conference › Abstract] Geometric Deep Learning in Medical Image Analysis, GeoMedIA 2022. Dummer, S., Strisciuglio, N. & Brune, C.https://openreview.net/pdf?id=YcjlgyX_Ur1Implicit Neural Representations for Generative Modeling of Living Cell Shapes (2022)[Working paper › Preprint]. ArXiv.org. Wiesner, D., Suk, J., Dummer, S., Svoboda, D. & Wolterink, J. M.https://doi.org/10.48550/arXiv.2207.06283Implicit Neural Representations for Generative Modeling of Living Cell Shapes (2022)In Medical Image Computing and Computer Assisted Intervention – MICCAI 2022: 25th International Conference, Singapore, September 18–22, 2022, Proceedings, Part IV (pp. 58-67) (Lecture Notes in Computer Science; Vol. 13434). Springer. Wiesner, D., Suk, J., Dummer, S., Svoboda, D. & Wolterink, J. M.https://doi.org/10.1007/978-3-031-16440-8_6
Pictures:
From the paper:
“A Mathematical Guide to Operator Learning” by Boullé and Townsend.
From the paper:
“High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion” by Lucka et al.
