Simon Koop

Simon M. Koop, Mark A. Peletier, Jacobus W. Portegies et al.

Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the drift and diffusion fields. By restricting our NSDE to be of the form of Langevin dynamics, and training it as a VAE, we obtain NSDEs that lend themselves to more elaborate analysis and to a wider range of visualisation techniques than a generic NSDE. More specifically, we obtain an energy landscape, the minima of which are in one-to-one correspondence with latent states underlying the used data. This not only allows us to detect states underlying the data dynamics in an unsupervised manner, but also to infer the distribution of time spent in each state according to the learned SDE. More in general, restricting an NSDE to Langevin dynamics enables the use of a large set of tools from computational molecular dynamics for the analysis of the obtained results.

Koen Minartz, Fleur Hendriks, Simon Martinus Koop et al.

Understanding the dynamics of pedestrian crowds is an outstanding challenge crucial for designing efficient urban infrastructure and ensuring safe crowd management. To this end, both small-scale laboratory and large-scale real-world measurements have been used. However, these approaches respectively lack statistical resolution and parametric controllability, both essential to discovering physical relationships underlying the complex stochastic dynamics of crowds. Here, we establish an investigation paradigm that offers laboratory-like controllability, while ensuring the statistical resolution of large-scale real-world datasets. Using our data-driven Neural Crowd Simulator (NeCS), which we train on large-scale data and validate against key statistical features of crowd dynamics, we show that we can perform effective surrogate crowd dynamics experiments without training on specific scenarios. We not only reproduce known experimental results on pairwise avoidance, but also uncover the vision-guided and topological nature of N-body interactions. These findings show how virtual experiments based on neural simulation enable data-driven scientific discovery.

Jonas Niederle, Simon Koop, Marc Pagès-Gallego et al.

Nanopore sequencing offers the ability for real-time analysis of long DNA sequences at a low cost, enabling new applications such as early detection of cancer. Due to the complex nature of nanopore measurements and the high cost of obtaining ground truth datasets, there is a need for nanopore simulators. Existing simulators rely on handcrafted rules and parameters and do not learn an internal representation that would allow for analysing underlying biological factors of interest. Instead, we propose VADA, a purely data-driven method for simulating nanopores based on an autoregressive latent variable model. We embed subsequences of DNA and introduce a conditional prior to address the challenge of a collapsing conditioning. We introduce an auxiliary regressor on the latent variable to encourage our model to learn an informative latent representation. We empirically demonstrate that our model achieves competitive simulation performance on experimental nanopore data. Moreover, we show we have learned an informative latent representation that is predictive of the DNA labels. We hypothesize that other biological factors of interest, beyond the DNA labels, can potentially be extracted from such a learned latent representation.

Koen Minartz, Yoeri Poels, Simon Koop et al.

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.