Related papers: The Dimensional Recurrence and Analyticity Method …

This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…

We have recently proposed a new regularization framework based on the loop-tree duality theorem. This theorem allows to rewrite loop level amplitudes in terms of tree-level structures and phase-space integrations. In consequence, it is…

In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…

Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this…

A triangular plate-bending element with a new multi-resolution analysis (MRA) is proposed and a novel multiresolution element method is hence presented. The MRA framework is formulated out of a displacement subspace sequence whose basis…

We develop an analytical synthesis that bridges data-driven Distributionally Robust Optimization (DRO) and Economic Decision Theory under Ambiguity (DTA). By reinterpreting standard regularization and DRO techniques as data-driven…

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…

Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…

Coarse-Grain Reconfigurable Arrays (CGRAs) provide flexibility and energy efficiency in accelerating compute-intensive loops. Existing compilation techniques often struggle with scalability, unable to map code onto large CGRAs. To address…

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…

We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…

Loop diagram calculations typically rely on reduction to a finite set of master integrals in $4 - 2\epsilon$ dimensions. It has been shown that for any problem, the masters can be chosen so that their coefficients are finite as $\epsilon…

We propose a novel distance-based regularization method for deep metric learning called Multi-level Distance Regularization (MDR). MDR explicitly disturbs a learning procedure by regularizing pairwise distances between embedding vectors…

We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts.…

A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…

The braking performance of the brake system is a target performance that must be considered for vehicle development. Apparent piston travel (APT) and drag torque are the most representative factors for evaluating braking performance. In…

We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…

Dimensional reduction~(DR) maps high-dimensional data into a lower dimensions latent space with minimized defined optimization objectives. The DR method usually falls into feature selection~(FS) and feature projection~(FP). FS focuses on…

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…