Generative model to improve the physical simulation of normalized seismic acceleration

Authors

  • Gottfried Jacquet Université Paris Saclay, CentraleSupélec, CNRS, ENS Paris-Saclay, Laboratoire de Mécanique Paris-Saclay UMR 9026, Gif-sur-Yvette, France https://orcid.org/0009-0000-6553-428X
  • Filippo Gatti Université Paris Saclay, CentraleSupélec, CNRS, ENS Paris-Saclay, Laboratoire de Mécanique Paris-Saclay UMR 9026, Gif-sur-Yvette, France https://orcid.org/0000-0001-7174-4048
  • Didier Clouteau Université Paris Saclay, CentraleSupélec, CNRS, ENS Paris-Saclay, Laboratoire de Mécanique Paris-Saclay UMR 9026, Gif-sur-Yvette, France

DOI:

https://doi.org/10.26443/seismica.v5i2.1775

Abstract

Earthquake physics-based simulations have revealed their accuracy limit in high-fidelity broadband strong ground motion scenario prediction. Earlier attempts leveraging AI tried to fill the gap between the low-frequency high-fidelity numerical simulation and the high-frequency accuracy and realism demanded in earthquake engineering. Our research is built on top of the SeismoALICE solution proposed by Gatti and Clouteau (2020), an AI generative approach that renders broadband (0-20 Hz) single-station accelerograms conditioned by low-frequency physics-based simulation outcomes. First, we developed a novel neural architecture based on Encoder, Decoder, and Discriminators that integrates Conformer's advanced attention techniques (Gulati et al., 2020), stabilising the training and producing realistic output for the generation. This novel architecture is trained according to Adversarial Learning Inference with Conditional Entropy (ALICE, Li et al., 2017). Second, our approach employs a similarity evaluation technique called Hyper-Spherical Loss (HSL) in the time domain and an adaptation of the Focal Frequency Loss (FFL) for time series. Our investigation demonstrates that Conformer architecture outperforms previous approaches in super-resolution of earthquake data, such as the STanford EArthquake Dataset (STEAD) Dataset (Mousavi et al., 2019). We finally showcase the enhanced strong motion synthesizer to predict the seismic response at the Cruas Nuclear Power Plant during the 2019 MW 4.9 Le Teil earthquake, providing insightful perspective for future large-scale applications as a downstream generative pipeline.

References

Aggarwal, C. C. (2018). Neural Networks and Deep Learning: A Textbook. Springer International Publishing. https://doi.org/10.1007/978-3-319-94463-0 DOI: https://doi.org/10.1007/978-3-319-94463-0

Aquib, T. A., & Mai, P. M. (2024). Broadband Ground-Motion Simulations with Machine-Learning-Based High-Frequency Waves from Fourier Neural Operators. Bulletin of the Seismological Society of America, 114(6), 2846–2868. https://doi.org/10.1785/0120240027 DOI: https://doi.org/10.1785/0120240027

Arjovsky, M., & Bottou, L. (2017). Towards Principled Methods for Training Generative Adversarial Networks. ArXiv:1701.04862 [Cs, Stat]. http://arxiv.org/abs/1701.04862

Becker, E., Pandit, P., Rangan, S., & Fletcher, A. K. (2022). Instability and Local Minima in GAN Training with Kernel Discriminators. arXiv. http://arxiv.org/abs/2208.09938 DOI: https://doi.org/10.52202/068431-1476

Belghazi, M. I., Baratin, A., Rajeswar, S., Ozair, S., Bengio, Y., Courville, A., & Hjelm, R. D. (2021). MINE: Mutual Information Neural Estimation. arXiv. https://doi.org/10.48550/arXiv.1801.04062

Bergmeister, A., Palgunadi, K. H., Bosisio, A., Ermert, L., Koroni, M., Perraudin, N., Dirmeier, S., & Meier, M.-A. (2024). High Resolution Seismic Waveform Generation using Denoising Diffusion. arXiv. http://arxiv.org/abs/2410.19343 DOI: https://doi.org/10.5194/egusphere-egu25-19236

Bi, Z., Nakata, N., Nakata, R., Ren, P., Wu, X., & Mahoney, M. W. (2025). Advancing data-driven broadband seismic wavefield simulation with multi-conditional diffusion model. arXiv. https://doi.org/10.48550/arXiv.2501.14348 DOI: https://doi.org/10.1109/TGRS.2025.3591881

Brock, A., Donahue, J., & Simonyan, K. (2019). Large Scale GAN Training for High Fidelity Natural Image Synthesis. ArXiv:1809.11096 [Cs, Stat]. http://arxiv.org/abs/1809.11096

Castro-Cruz, D., Gatti, F., & Lopez-Caballero, F. (2021). High-fidelity broadband prediction of regional seismic response: a hybrid coupling of physics-based synthetic simulation and empirical Green functions. Natural Hazards, 108(2), 1997–2031. https://doi.org/10.1007/s11069-021-04766-x DOI: https://doi.org/10.1007/s11069-021-04766-x

Castro-Cruz, D., Gatti, F., Lopez-Caballero, F., Hollender, F., El Haber, E., & Causse, M. (2022). Blind broad-band (0–10 Hz) numerical prediction of the 3-D near field seismic response of an M W6.0 extended fault scenario: application to the nuclear site of Cadarache (France). Geophysical Journal International, 232(1), 581–600. https://doi.org/10.1093/gji/ggac346 DOI: https://doi.org/10.1093/gji/ggac346

Donahue, J., Krähenbühl, P., & Darrell, T. (2017). Adversarial Feature Learning (7 type: article). arXiv. https://doi.org/10.48550/arXiv.1605.09782

Donahue, J., & Simonyan, K. (2019). Large Scale Adversarial Representation Learning. arXiv. https://doi.org/10.48550/arXiv.1907.02544

Dumoulin, V., Belghazi, I., Poole, B., Mastropietro, O., Lamb, A., Arjovsky, M., & Courville, A. (2017). Adversarially Learned Inference. arXiv. https://doi.org/10.48550/arXiv.1606.00704

Esfahani, R. D. D., Cotton, F., Ohrnberger, M., & Scherbaum, F. (2023). TFCGAN: Nonstationary Ground-Motion Simulation in the Time–Frequency Domain Using Conditional Generative Adversarial Network (CGAN) and Phase Retrieval Methods. Bulletin of the Seismological Society of America, 113(1), 453–467. https://doi.org/10.1785/0120220068 DOI: https://doi.org/10.1785/0120220068

Florez, M. A., Caporale, M., Buabthong, P., Ross, Z. E., Asimaki, D., & Meier, M.-A. (2020). Data-driven Accelerogram Synthesis using Deep Generative Models. ArXiv:2011.09038 [Physics, Stat]. http://arxiv.org/abs/2011.09038

Gabrielidis, H., Gatti, F., & Vialle, S. (2025). Physics-based super-resolved simulation of 3D elastic wave propagation adopting scalable Diffusion Transformer. Computer Physics Communications, 109930. https://doi.org/10.1016/j.cpc.2025.109930 DOI: https://doi.org/10.1016/j.cpc.2025.109930

Gatti, F., & Clouteau, D. (2020). Towards blending Physics-Based numerical simulations and seismic databases using Generative Adversarial Network. Computer Methods in Applied Mechanics and Engineering, 372, 113421. https://doi.org/10.1016/j.cma.2020.113421 DOI: https://doi.org/10.1016/j.cma.2020.113421

Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., & Bengio, Y. (2014). Generative Adversarial Networks. ArXiv:1406.2661 [Cs, Stat]. http://arxiv.org/abs/1406.2661

Gulati, A., Qin, J., Chiu, C.-C., Parmar, N., Zhang, Y., Yu, J., Han, W., Wang, S., Zhang, Z., Wu, Y., & Pang, R. (2020). Conformer: Convolution-augmented Transformer for Speech Recognition. arXiv. http://arxiv.org/abs/2005.08100 DOI: https://doi.org/10.21437/Interspeech.2020-3015

Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., & Courville, A. (2017). Improved Training of Wasserstein GANs. ArXiv:1704.00028 [Cs, Stat]. http://arxiv.org/abs/1704.00028

Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., & Hochreiter, S. (2018). GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium (6 type: article). arXiv. https://doi.org/10.48550/arXiv.1706.08500

Hoffmann, J., Borgeaud, S., Mensch, A., Buchatskaya, E., Cai, T., Rutherford, E., Casas, D. de L., Hendricks, L. A., Welbl, J., Clark, A., Hennigan, T., Noland, E., Millican, K., Driessche, G. van den, Damoc, B., Guy, A., Osindero, S., Simonyan, K., Elsen, E., … Sifre, L. (2022). Training Compute-Optimal Large Language Models. arXiv. https://doi.org/10.48550/arXiv.2203.15556 DOI: https://doi.org/10.52202/068431-2176

Huang, L., Liu, X., Lang, B., Yu, A. W., Wang, Y., & Li, B. (2017). Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks. arXiv. https://doi.org/10.48550/arXiv.1709.06079 DOI: https://doi.org/10.1609/aaai.v32i1.11768

Ichimura, T., Fujita, K., Koyama, K., Kikuchi, Y., Kusakabe, R., Minami, K., Inoue, H., Nishizawa, S., Tsuji, M., Nishiki, T., Hori, M., Maddegedara, L., & Ueda, N. (2021). Fast scalable implicit solver with convergence of equation-based modeling and data-driven learning: earthquake city simulation on low-order unstructured finite element. Proceedings of the Platform for Advanced Scientific Computing Conference, 1–12. https://doi.org/10.1145/3468267.3470616 DOI: https://doi.org/10.1145/3468267.3470616

Jacquet, G. (2025). jacquetgottfried/SeismoALICE-v2: SeismoALICE on scaled data [Software]. Zenodo. https://doi.org/10.5281/zenodo.15799533

Kamae, K., Irikura, K., & Pitarka, A. (1998). A technique for simulating strong ground motion using hybrid Green’s function. Bulletin of the Seismological Society of America, 88(2), 357–367. https://doi.org/10.1785/BSSA0880020357 DOI: https://doi.org/10.1785/BSSA0880020357

Kumar, K., Kumar, R., de Boissiere, T., Gestin, L., Teoh, W. Z., Sotelo, J., de Brebisson, A., Bengio, Y., & Courville, A. (2019). MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis. arXiv. https://doi.org/10.48550/arXiv.1910.06711

Lee, M., & Seok, J. (2020). Regularization Methods for Generative Adversarial Networks: An Overview of Recent Studies (p. 18). https://doi.org/10.48550/arXiv.2005.09165

Lehmann, F., Gatti, F., Bertin, M., & Clouteau, D. (2022). Machine learning opportunities to conduct high-fidelity earthquake simulations in multi-scale heterogeneous geology. Frontiers in Earth Science, 10. https://www.frontiersin.org/articles/10.3389/feart.2022.1029160 DOI: https://doi.org/10.3389/feart.2022.1029160

Lehmann, F., Gatti, F., Bertin, M., & Clouteau, D. (2023). Fourier Neural Operator Surrogate Model to Predict 3D Seismic Waves Propagation. arXiv. http://arxiv.org/abs/2304.10242 DOI: https://doi.org/10.7712/120223.10339.20362

Li, C., Liu, H., Chen, C., Pu, Y., Chen, L., Henao, R., & Carin, L. (2017). ALICE: Towards Understanding Adversarial Learning for Joint Distribution Matching. ArXiv:1709.01215 [Cs, Stat]. http://arxiv.org/abs/1709.01215

McCallen, D., Petersson, A., Rodgers, A., Pitarka, A., Miah, M., Petrone, F., Sjogreen, B., Abrahamson, N., & Tang, H. (2021). EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers part I: Computational models and workflow. Earthquake Spectra, 37(2). https://doi.org/10.1177/8755293020970982 DOI: https://doi.org/10.1177/8755293020970982

McCallen, D., Petrone, F., Miah, M., Pitarka, A., Rodgers, A., & Abrahamson, N. (2021). EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers, part II: Regional simulations of building response. Earthquake Spectra, 37(2). https://doi.org/10.1177/8755293020970980 DOI: https://doi.org/10.1177/8755293020970980

Miyato, T., Kataoka, T., Koyama, M., & Yoshida, Y. (2018). Spectral Normalization for Generative Adversarial Networks. ArXiv:1802.05957 [Cs, Stat]. http://arxiv.org/abs/1802.05957

Mousavi, S. M., Ellsworth, W. L., Zhu, W., Chuang, L. Y., & Beroza, G. C. (2020). Earthquake transformer—an attentive deep-learning model for simultaneous earthquake detection and phase picking. Nature Communications, 11(1), 3952. https://doi.org/10.1038/s41467-020-17591-w DOI: https://doi.org/10.1038/s41467-020-17591-w

Mousavi, S. M., Sheng, Y., Zhu, W., & Beroza, G. C. (2019). STanford EArthquake Dataset (STEAD): A Global Data Set of Seismic Signals for AI. IEEE Access, 7, 179464–179476. https://doi.org/10.1109/ACCESS.2019.2947848 DOI: https://doi.org/10.1109/ACCESS.2019.2947848

Nakata, R., Nakata, N., Ren, P., Bi, Z., Lacour, M., Erichson, B., & Mahoney, M. W. (2025). Simulating seismic wavefields using generative artificial intelligence. The Leading Edge, 44(2), 123–132. https://doi.org/10.1190/tle44020123.1 DOI: https://doi.org/10.1190/tle44020123.1

Paolucci, R., Gatti, F., Infantino, M., Smerzini, C., Özcebe, A. G., & Stupazzini, M. (2018). Broadband Ground Motions from 3D Physics‐Based Numerical Simulations Using Artificial Neural NetworksBroadband Ground Motions from 3D PBSs Using ANNs. Bulletin of the Seismological Society of America, 108(3), 1272–1286. https://doi.org/10.1785/0120170293 DOI: https://doi.org/10.1785/0120170293

Paolucci, R., Mazzieri, I., Smerzini, C., & Stupazzini, M. (2014). Physics-Based Earthquake Ground Shaking Scenarios in Large Urban Areas. In A. Ansal (Ed.), Perspectives on European Earthquake Engineering and Seismology (Vol. 34, pp. 331–359). Springer International Publishing. https://doi.org/10.1007/978-3-319-07118-3_10 DOI: https://doi.org/10.1007/978-3-319-07118-3_10

Pitarka, A., & Mellors, R. (2021). Using Dense Array Waveform Correlations to Build a Velocity Model with Stochastic Variability. Bulletin of the Seismological Society of America, 111(4), 2021–2041. https://doi.org/10.1785/0120200206 DOI: https://doi.org/10.1785/0120200206

Rekoske, J. M., Gabriel, A.-A., & May, D. A. (2023-08). Instantaneous physics-based ground motion maps using reduced-order modeling. Journal of Geophysical Research: Solid Earth, 128(8), e2023JB026975. https://doi.org/10.1029/2023JB026975 DOI: https://doi.org/10.1029/2023JB026975

Salimans, T., & Kingma, D. P. (2016). Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks. https://doi.org/10.48550/arXiv.1602.07868

Smerzini, C., & Villani, M. (2012). Broadband Numerical Simulations in Complex Near-Field Geological Configurations: The Case of the 2009 Mw 6.3 L’Aquila Earthquake. Bulletin of the Seismological Society of America, 102(6), 2436–2451. https://doi.org/10.1785/0120120002 DOI: https://doi.org/10.1785/0120120002

Smith, L. N. (2017). Cyclical Learning Rates for Training Neural Networks. arXiv. http://arxiv.org/abs/1506.01186 DOI: https://doi.org/10.1109/WACV.2017.58

Sochala, P., De Martin, F., & Le Maître, O. (2020). MODEL REDUCTION FOR LARGE-SCALE EARTHQUAKE SIMULATION IN AN UNCERTAIN 3D MEDIUM. International Journal for Uncertainty Quantification, 10(2), 101–127. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020031165 DOI: https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020031165

Touhami, S., Gatti, F., Lopez-Caballero, F., Cottereau, R., De Abreu Corrêa, L., Aubry, L., & Clouteau, D. (2022). SEM3D: A 3D High-Fidelity Numerical Earthquake Simulator for Broadband (0–10 Hz) Seismic Response Prediction at a Regional Scale. Geosciences, 12(3), 112. https://doi.org/10.3390/geosciences12030112 DOI: https://doi.org/10.3390/geosciences12030112

Wright, A., & Fayaz, J. (2026). Structured generative modelling of earthquake response spectra with hierarchical latent variables in hyperbolic geometry. Scientific Reports, 16(1), 906. https://doi.org/10.1038/s41598-025-29902-6 DOI: https://doi.org/10.1038/s41598-025-29902-6

Zhang, H., Goodfellow, I., Metaxas, D., & Odena, A. (2019). Self-Attention Generative Adversarial Networks. arXiv. http://arxiv.org/abs/1805.08318

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2026-09-02

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Jacquet, G., Gatti, F., & Clouteau, D. (2026). Generative model to improve the physical simulation of normalized seismic acceleration. Seismica, 5(2). https://doi.org/10.26443/seismica.v5i2.1775

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Vol. 5 No. 2 (2026)

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Copyright (c) 2026 Gottfried Jacquet, Filippo Gatti, Didier Clouteau

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