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In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
Applications of Reinforcement Learning (RL), in which agents learn to make a sequence of decisions despite lacking complete information about the latent states of the controlled system, that is, they act under partial observability of the…
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
We consider the problem of learning a non-deterministic probabilistic system consistent with a given finite set of positive and negative tree samples. Consistency is defined with respect to strong simulation conformance. We propose learning…
Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…
Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. In several aspects, PLD is close to Decision Tree/Random Forest methods, but it differs significantly in…
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of…
We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective functionals and the resulting high-dimensional and…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
In this paper, we develop approximate dynamic programming methods for stochastic systems modeled as Markov Decision Processes, given both soft performance criteria and hard constraints in a class of probabilistic temporal logic called…
Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…
As further progress in the accurate and efficient computation of coupled partial differential equations (PDEs) becomes increasingly difficult, it has become highly desired to develop new methods for such computation. In deviation from…
The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…