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Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
Considering uncertainties and disturbances is an important, yet challenging, step in successful decision making. The problem becomes more challenging in safety-constrained environments. In this paper, we propose a robust and safe trajectory…
This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations…
This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…
Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. A sliding mode is coped with differential-algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with…
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…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify…
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…
Gradient-based optimization of neural differential equations and other parameterized dynamical systems fundamentally relies on the ability to differentiate numerical solutions with respect to model parameters. In stiff systems, it has been…
Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require…
We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations (DAEs) w.r.t. the time variable which yields an optimally stable system. This is used within a Petrov-Galerkin method to derive…