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In this work we introduce a new framework for performing temporal predictions in the presence of uncertainty. It is based on a simple idea of disentangling components of the future state which are predictable from those which are inherently…
We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…
The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable,…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
One of the main questions regarding complex systems at large scales concerns the effective interactions and driving forces that emerge from the detailed microscopic properties. Coarse-grained models aim to describe complex systems in terms…
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…
This paper considers learning the hidden causal network of a linear networked dynamical system (NDS) from the time series data at some of its nodes -- partial observability. The dynamics of the NDS are driven by colored noise that generates…
Scalable probabilistic modeling and prediction in high dimensional multivariate time-series is a challenging problem, particularly for systems with hidden sources of dependence and/or homogeneity. Examples of such problems include dynamic…
Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…
Deep learning has taken part in the competition since not long ago to learn and identify phase transitions in physical systems such as many body quantum systems, whose underlying lattice structures are generally regular as they're in…
We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if…
Discovering the underlying behavior of complex systems is an important topic in many science and engineering disciplines. In this paper, we propose a novel neural network framework, finite difference neural networks (FDNet), to learn…
Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into…