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Deploying learned control policies in real-world environments poses a fundamental challenge. When system dynamics change unexpectedly, performance degrades until models are retrained on new data. We introduce Reflexive World Models (RWM), a…

In this work, we propose a novel layerwise adaptive construction method for neural network architectures. Our approach is based on a goal--oriented dual-weighted residual technique for the optimal control of neural differential equations.…

We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed…

In this work, a flexible higher-order space-time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in…

This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…

While widely recognized as one of the most substantial weather forecasting methodologies, Numerical Weather Prediction (NWP) usually suffers from relatively coarse resolution and inevitable bias due to tempo-spatial discretization, physical…

We present a new framework for solving general topology optimization (TO) problems that find an optimal material distribution within a design space to maximize the performance of a structure while satisfying design constraints. These…

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

In this work, we derive two-sided a posteriori error estimates for the dual-weighted residual (DWR) method. We consider both single and multiple goal functionals. Using a saturation assumption, we derive lower bounds yielding the efficiency…

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that…

The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint…

This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…

In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…

We present an anisotropic goal-oriented error estimator based on the Dual Weighted Residual (DWR) method for time-dependent convection-diffusion-reaction (CDR) equations. Using anisotropic interpolation operators the estimator is…

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…

This paper investigates the multi-UAV multi-task coordination problem in infrastructure-less emergency scenarios, where UAVs collaboratively are required to jointly perform aerial image acquisition and ground-user communication. To tackle…

With the continuous improvement of the performance of object detectors via advanced model architectures, imbalance problems in the training process have received more attention. It is a common paradigm in object detection frameworks to…

Diffusion models have recently emerged as effective generative frameworks for trajectory optimization, capable of producing high-quality and diverse solutions. However, training these models in a purely data-driven manner without explicit…

Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this paper, we propose new reformulation techniques for…

Deep metric learning (DML) has received much attention in deep learning due to its wide applications in computer vision. Previous studies have focused on designing complicated losses and hard example mining methods, which are mostly…