Related papers: Convex Nonparametric Formulation for Identificatio…
A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
Feature identification is an important task in many fluid dynamics applications and diverse methods have been developed for this purpose. These methods are based on a physical understanding of the underlying behavior of the flow in the…
We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…
This paper considers the problem of regulating a linear dynamical system to the solution of a convex optimization problem with an unknown or partially-known cost. We design a data-driven feedback controller - based on gradient flow dynamics…
In this paper, we study the flux identification problem for a nonlinear time-fractional viscoelastic equation with a general source function based on the boundary measurements. We prove that the direct problem is well-posed, i.e., the…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…
We propose a convex optimization procedure for black-box identification of nonlinear state-space models for systems that exhibit stable limit cycles (unforced periodic solutions). It extends the "robust identification error" framework in…
We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design…
We employ the principle of minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first…
This paper presents three main contributions to the field of multi-step system identification. First, drawing inspiration from Neural Network (NN) training, it introduces a tool for solving identification problems by leveraging first-order…
Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal…
Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of…
This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…