Related papers: Stochastic embeddings of dynamical phenomena throu…

Stochastic dynamical systems are ubiquitous in physics, biology, and engineering, where both deterministic drifts and random fluctuations govern system behavior. Learning these dynamics from data is particularly challenging in…

We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…

Learning stochastic models of dynamical systems from observed data is of interest in many scientific fields. Here, we propose a new method for this task within the family of dynamical variational autoencoders. The proposed double projection…

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…

Neural Stochastic Differential Equations model a dynamical environment with neural nets assigned to their drift and diffusion terms. The high expressive power of their nonlinearity comes at the expense of instability in the identification…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Local causal states are latent representations that capture organized pattern and structure in complex spatiotemporal systems. We expand their functionality, framing them as spacetime autoencoders. Previously, they were only considered as…

Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…

The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…

Detecting anomalous edges and nodes in dynamic networks is critical in various areas, such as social media, computer networks, and so on. Recent approaches leverage network embedding technique to learn how to generate node representations…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…

Variational autoencoders employ an encoding neural network to generate a probabilistic representation of a data set within a low-dimensional space of latent variables followed by a decoding stage that maps the latent variables back to the…

Derivation of the probability density evolution provides invaluable insight into the behavior of many stochastic systems and their performance. However, for most real-time applica-tions, numerical determination of the probability density…

Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains a challenging yet necessary prerequisite for designing efficient numerical approaches. Machine learning methods have the potential…

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…

Learning the structure of dependencies among multiple random variables is a problem of considerable theoretical and practical interest. Within the context of Bayesian Networks, a practical and surprisingly successful solution to this…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…

We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…

Recent advances in deep learning have led to a paradigm shift in the field of reversible steganography. A fundamental pillar of reversible steganography is predictive modelling which can be realised via deep neural networks. However,…