Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929499315109888 |
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| author | Minartz, Koen Poels, Yoeri Koop, Simon Menkovski, Vlado |
| author_facet | Minartz, Koen Poels, Yoeri Koop, Simon Menkovski, Vlado |
| contents | Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that incorporating domain symmetries in deterministic neural simulators can substantially improve their accuracy, sample efficiency, and parameter efficiency. However, to incorporate symmetries in probabilistic neural simulators that can simulate stochastic phenomena, we need a model that produces equivariant distributions over trajectories, rather than equivariant function approximations. In this paper, we propose Equivariant Probabilistic Neural Simulation (EPNS), a framework for autoregressive probabilistic modeling of equivariant distributions over system evolutions. We use EPNS to design models for a stochastic n-body system and stochastic cellular dynamics. Our results show that EPNS considerably outperforms existing neural network-based methods for probabilistic simulation. More specifically, we demonstrate that incorporating equivariance in EPNS improves simulation quality, data efficiency, rollout stability, and uncertainty quantification. We conclude that EPNS is a promising method for efficient and effective data-driven probabilistic simulation in a diverse range of domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14286 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics Minartz, Koen Poels, Yoeri Koop, Simon Menkovski, Vlado Machine Learning Artificial Intelligence Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that incorporating domain symmetries in deterministic neural simulators can substantially improve their accuracy, sample efficiency, and parameter efficiency. However, to incorporate symmetries in probabilistic neural simulators that can simulate stochastic phenomena, we need a model that produces equivariant distributions over trajectories, rather than equivariant function approximations. In this paper, we propose Equivariant Probabilistic Neural Simulation (EPNS), a framework for autoregressive probabilistic modeling of equivariant distributions over system evolutions. We use EPNS to design models for a stochastic n-body system and stochastic cellular dynamics. Our results show that EPNS considerably outperforms existing neural network-based methods for probabilistic simulation. More specifically, we demonstrate that incorporating equivariance in EPNS improves simulation quality, data efficiency, rollout stability, and uncertainty quantification. We conclude that EPNS is a promising method for efficient and effective data-driven probabilistic simulation in a diverse range of domains. |
| title | Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2305.14286 |