Related papers: Machine learning-based moment closure model for th…
Finding reduced models of spatially-distributed chemical reaction networks requires an estimation of which effective dynamics are relevant. We propose a machine learning approach to this coarse graining problem, where a maximum entropy…
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…
A Boltzmann machine whose effective "temperature" can be dynamically "cooled" provides a stochastic neural network realization of simulated annealing, which is an important metaheuristic for solving combinatorial or global optimization…
This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with…
A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions…
In this work we propose a generalization of the Moment Guided Monte Carlo method developed in [11]. This approach permits to reduce the variance of the particle methods through a matching with a set of suitable macroscopic moment equations.…
Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…
We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment…
Classification of sequence data is the topic of interest for dynamic Bayesian models and Recurrent Neural Networks (RNNs). While the former can explicitly model the temporal dependencies between class variables, the latter have a capability…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
Time series forecasts are widely used to inform decisions. Human decision-makers interpret these forecasts, incorporate prior experience and uncertainty about future outcomes, and then make a decision. In this paper, we propose a new…
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
One of the biggest challenges for simulating the Boltzmann equation is the evaluation of fivefold collision integral. Given the recent successes of deep learning and the availability of efficient tools, it is an obvious idea to try to…
With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics a second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows the explicit, highly parallelisable LBM to…
In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from the initial data and collision kernel is studied. Well-posedness and long-time behavior - exponential decay to the global equilibrium - of the…
The multi-scale nature of gaseous flows poses tremendous difficulties for theoretical and numerical analysis. The Boltzmann equation, while possessing a wider applicability than hydrodynamic equations, requires significantly more…
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…
We propose a multiple relaxation time Boltzmann equation collision model by systematically assigning a separate relaxation time to each of the central moments of the distribution function. The Chapman-Enskog calculation leads to correct…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…