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Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Deep Boltzmann Machines (DBMs) are generative neural networks with these desired properties. We integrate a DBM…
Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be…
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…
Mathematical models of physical systems are subject to many uncertainties such as measurement errors and uncertain initial and boundary conditions. After accounting for these uncertainties, it is often revealed that discrepancies between…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
The unprecedented availability of large-scale datasets in neuroscience has spurred the exploration of artificial deep neural networks (DNNs) both as empirical tools and as models of natural neural systems. Their appeal lies in their ability…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…
Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…
Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…
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…
Deep neural networks (DNNs) have made a revolution in numerous fields during the last decade. However, in tasks with high safety requirements, such as medical or autonomous driving applications, providing an assessment of the models…
Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological…
On a daily investment decision in a security market, the price earnings (PE) ratio is one of the most widely applied methods being used as a firm valuation tool by investment experts. Unfortunately, recent academic developments in financial…
Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditional distributions and can miss larger-scale patterns in how…
Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE),…
In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…
Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…
This paper proposes the DnD Filter, a differentiable filter that utilizes diffusion models for state estimation of dynamic systems. Unlike conventional differentiable filters, which often impose restrictive assumptions on process noise…
Ordinary differential equations (ODEs) are widely used to describe the time evolution of natural phenomena across various scientific fields. Estimating the parameters of these systems from data is a challenging task, particularly when…