Related papers: Adjoint Variable Method for Transient Nonlinear El…
The paper contributes to strengthening the relation between machine learning and the theory of differential equations. In this context, the inverse problem of fitting the parameters, and the initial condition of a differential equation to…
This work presents the Second-Order Sensitivity Analysis Methodology (2nd-ASAM) for nonlinear systems. This methodology yields exactly and efficiently the second-order functional derivatives of system responses (associated with physical,…
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…
Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
The paper deals with joint state and parameter estimation for nonlinear continuous-time systems. Based on a guaranteed LPV approximation, the set adaptive observers design problem is solved avoiding the exponential complexity obstruction…
Certain neural network architectures, in the infinite-layer limit, lead to systems of nonlinear differential equations. Motivated by this idea, we develop a framework for analyzing time signals based on non-autonomous dynamical equations.…
The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas…
In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive…
Dynamic optimization is currently limited by sensitivity computations that require information from full forward and adjoint wave fields. Since the forward and adjoint solutions are computed in opposing time directions, the forward solution…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
An adjoint-based procedure to determine weaknesses, or, more generally the material properties of structures is developed and tested. Given a series of force and deformation/strain measurements, the material properties are obtained by…
In the optimization of turbomachinery components, shape sensitivities for fluid dynamical objective functions have been used for a long time. As peak stress is not a differential func- tional of the shape, such highly efficient procedures…
Motivated by the pressing challenges in the digital twin development for biomanufacturing systems, we introduce an adjoint sensitivity analysis (SA) approach to expedite the learning of mechanistic model parameters. In this paper, we…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
Meta-optics promises compact, high-performance imaging and color routing. However, designing high-performance structures is a high-dimensional optimization problem: mapping a desired optical output back to a physical 3D structure requires…
Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulations for design. However, the conventional adjoint method breaks down for scale-resolving simulations like large-eddy simulation (LES) or direct…
This document, as the title stated, is meant to provide a vectorized implementation of adjoint dynamics calculation for Graph Convolutional Neural Ordinary Differential Equations (GCDE). The adjoint sensitivity method is the gradient…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…
In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some…