The Real-Time Iteration (RTI) is an online nonlinear model predictive control algorithm that performs a single Sequential Quadratic Programming (SQP) per sampling time.

Optimization and Control

We propose a new neural network based large eddy simulation framework for the incompressible Navier-Stokes equations based on the paradigm "discretize first, filter and close next".

Numerical Analysis Numerical Analysis Fluid Dynamics 65 (Primary), 76, 35 (Secondary)

Different from most studied distributed optimization problems with time-invariant objective functions and constraints, the optimal solution in this paper is time varying and forms a trajectory.

Optimization and Control

As showed in (Fiedler, 1990), any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix.

Numerical Analysis 65F15, 65G50, 15-04, 15B99

We also study the problem without restriction on the optimal plan, and provide lower and upper bounds for the value of the Gromov-Wasserstein distance between Gaussian distributions.

Probability

We introduce Optimistix: a nonlinear optimisation library built in JAX and Equinox.

Optimization and Control Mathematical Software

A conjecture of Marton, widely known as the polynomial Freiman-Ruzsa conjecture, was recently proved by Gowers, Green, Manners and Tao for any bounded-torsion Abelian group $G$.

Combinatorics

The Hadamard conjecture states that Hadamard matrices of order $n$ exist whenever $n$ is $1$, $2$, or a multiple of $4$.

Combinatorics

PySINDy is a Python package for the discovery of governing dynamical systems models from data.

Dynamical Systems Computational Physics

Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic.

Combinatorics Discrete Mathematics Logic in Computer Science Logic