Related papers: Some Critical Issues for the "Equation-Free" Appro…

Ecologists increasingly rely on Bayesian methods to fit capture-recapture models. Capture-recapture models are used to estimate abundance while accounting for imperfect detectability in individual-level data. A variety of implementations…

Multiscale modeling of material properties has emerged as one of the grand challenges in material science and engineering. We provide a comprehensive, though not exhaustive, overview of the current status of multiscale simulations of…

This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…

In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related…

Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…

In this paper, we develop a novel unfitted multiscale framework that combines two separate scales represented by only one single computational mesh. Our framework relies on a mixed zooming technique where we zoom at regions of interest to…

In this paper a new multiscale modeling technique is proposed. It relies on a recently introduced measure-theoretic approach, which allows to manage the microscopic and the macroscopic scale under a unique framework. In the resulting…

Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…

We consider the problem of finding a policy that maximizes an expected reward throughout the trajectory of an agent that interacts with an unknown environment. Frequently denoted Reinforcement Learning, this framework suffers from the need…

We consider model-based derivative-free optimization (DFO) for large-scale problems, based on iterative minimization in random subspaces. We provide the first worst-case complexity bound for such methods for convergence to approximate…

Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…

This study established a quantum-classical hybrid framework that integrates quantum computing paradigm with meshfree finite particle method. By harnessing quantum superposition and entanglement, it hybridized the critical computational…

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript…

Complex black-box predictive models may have high performance, but lack of interpretability causes problems like lack of trust, lack of stability, sensitivity to concept drift. On the other hand, achieving satisfactory accuracy of…

When making predictions about ecosystems, we often have available a number of different ecosystem models that attempt to represent their dynamics in a detailed mechanistic way. Each of these can be used as simulators of large-scale…

Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

The pedestrian flow is one of the most complex systems, involving large populations of interacting agents. Models at microscopic and macroscopic scales offer different advantages for studying related problems. In general, microscopic models…

This research focuses on an innovative task of extracting equations from incomplete data, moving away from traditional methods used for complete solutions. The study addresses the challenge of extracting equations from data, particularly in…