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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…

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic…

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…

Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…

System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a…

One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many…

We propose a novel framework for Network Stochastic Differential Equations (N-SDE), where each node in a network is governed by an SDE influenced by interactions with its neighbors. The evolution of each node is driven by the interplay of…

A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens' theorem provides conditions for when it is possible to augment these…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

Understanding the training dynamics of deep learning models is perhaps a necessary step toward demystifying the effectiveness of these models. In particular, how do data from different classes gradually become separable in their feature…

The manifold hypothesis suggests that high-dimensional neural time series lie on a low-dimensional manifold shaped by simpler underlying dynamics. To uncover this structure, latent dynamical variable models such as state-space models,…

Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two…

Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…

Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…