Related papers: Goal-Oriented Adaptivity and Multilevel Preconditi…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the Frank-Oseen elastic free-energy model of nematic and cholesteric liquid crystals, where the required unit-length…
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact…
In recent years several learning approaches to point goal navigation in previously unseen environments have been proposed. They vary in the representations of the environments, problem decomposition, and experimental evaluation. In this…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
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…
The efficient approximation of quantity of interest derived from PDEs with lognormal diffusivity is a central challenge in uncertainty quantification. In this study, we propose a multilevel quasi-Monte Carlo framework to approximate…
In this paper we study adaptive discretization of the iteratively regularized Gauss-Newton method IRGNM with an a posteriori (discrepancy principle) choice of the regularization parameter in each Newton step and of the stopping index. We…
We design a class of variable metric evolution strategies well suited for high-dimensional problems. We target problems with many variables, not (necessarily) with many objectives. The construction combines two independent developments:…
This paper provides the first provable $\mathcal{O}(N \log N)$ algorithms for the linear system arising from the direct finite element discretization of the fourth-order equation with different boundary conditions on unstructured grids of…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
We consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation interconnecting a finite element discretization, the…
Many engineering problems have multiple objectives, and the overall aim is to optimize a non-linear function of these objectives. In this paper, we formulate the problem of maximizing a non-linear concave function of multiple long-term…
A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive,…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…
We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…
Bilevel optimization aims to optimize an outer objective function that depends on the solution to an inner optimization problem. It is routinely used in Machine Learning, notably for hyperparameter tuning. The conventional method to compute…
We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a robust full-space interior-point (IP)-Gauss-Newton…