Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of PDE into loss function network-based surrogate model unknown state, PINNs can seamlessly blend measurement data with physical constraints. Here, we extend this framework to PDE-constrained opti...

We propose a discrete transition-based reweighting analysis method (dTRAM) for analyzing configuration-space-discretized simulation trajectories produced at different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAM provides maximum-likelihood estimates of stationary quantities (probabilities, free energies, expectation values) at any thermodynamic state. In contrast to the weighte...

One method to solve topology optimization problems is the topological derivative. This approach has some drawbacks: it is limited to simple problems, we do not know how to fill holes, ... To overcome these limitations, an extension of the adjoint method is presented. Named the numerical vault, it allows us to consider new fields of applications and to explore new theoretical investigations in t...

The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be ...

Traditional transmission travel-time tomography hinges on ray tracing techniques. We propose a PDE-based Eulerian approach to travel-time tomography so that we can avoid the cumbersome ray-tracing. We start from the eikonal equation, define a mismatching functional and derive the gradient of the nonlinear functional by an adjoint state method. The resulting forward and adjoint problems can be e...

This paper develops an adaptive finite element method for shape optimization in stationary incompressible flow with damping. The continuous shape gradient of an objective functional with respect to the boundary shape is derived by using the adjoint equation method and a function space parametrization technique. A projection a-posteriori error estimator is proposed, which can be computed easily ...

Abstract: This paper addresses the numerical solution of optimal control problems for systems described by ordinary differential equations with control constraints. The state equation is discretized by a general explicit Runge-Kutta scheme and the controls are approximated by functions that are piecewise polynomial, but not necessarily continuous. We then propose an approximate gradient project...

In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems (MOOCP)'s is introduced‎. ‎In this approach‎, ‎first a discretized form of the time-control space is considered and then‎, ‎a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using ...

We present a spatial domain decomposition (DD) method for the solution of discretized parabolic linear–quadratic optimal control problems. Our DD preconditioners are extensions of Neumann-Neumann DD methods, which have been successfully applied to the solution of single elliptic partial differential equations and of linear–quadratic optimal control problems governed by elliptic equations. We us...