Publications related to Millennium Prize Problems

Hands-on tasks make learning visible: a learning analytics lens on the development of mechanistic problem-solving expertise in makerspaces

Richard Lee Davis, Bertrand Roland Schneider

This study investigated the impact of participating in a year-long digital-fabrication course on high-school seniors' problem-solving skills, with a focus on problems involving mechanistic systems. The research questions centered on whether working in a ma ...

New York2023

Mean Field Type Control With Species Dependent Dynamics via Structured Tensor Optimization

Isabel Haasler, Axel Ringh, Yiqiang Chen

In this letter we consider mean field type control problems with multiple species that have different dynamics. We formulate the discretized problem using a new type of entropy-regularized multimarginal optimal transport problems where the cost is a decomp ...

2023

The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Klaus Jansen, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

Knapsack and Subset Sum with Small Items

Adam Teodor Polak, Lars Rohwedder

Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various parameters. In t ...

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Jan Sickmann Hesthaven, Niccolo' Discacciati, Deep Ray

High-order numerical solvers for conservation laws suffer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amoun ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

A mathematical model of the human heart

Alfio Quarteroni

In this paper, we present a mathematical model able to simulate the cardiac function. We first describe the basic physical principles behind the mathematical equations, then we illustrate a few examples of application to problems of clinical relevance. ...

PENSIERO SCIENTIFICO EDITOR2020

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Millennium Prize Problems

Hands-on tasks make learning visible: a learning analytics lens on the development of mechanistic problem-solving expertise in makerspaces

Mean Field Type Control With Species Dependent Dynamics via Structured Tensor Optimization

The double exponential runtime is tight for 2-stage stochastic ILPs

Continuation Methods For Riemannian Optimization

Knapsack and Subset Sum with Small Items

Atomistic modeling of the solid-liquid interface of metals and alloys

Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

Constraint-aware neural networks for Riemann problems

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

A mathematical model of the human heart

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Chat with Graph Search

Constraint-aware neural networks for Riemann problems

The double exponential runtime is tight for 2-stage stochastic ILPs

Atomistic modeling of the solid-liquid interface of metals and alloys

Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

A mathematical model of the human heart

Knapsack and Subset Sum with Small Items

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Continuation Methods For Riemannian Optimization