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

Dynamical Systems Computational Physics

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools.

Numerical Analysis Numerical Analysis Computational Physics

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning.

Statistics Theory Econometrics Statistics Theory

We consider the problem of optimally executing an order involving multiple crypto-assets, sometimes called tokens, on a network of multiple constant function market makers (CFMMs).

Optimization and Control Trading and Market Microstructure

The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as Python and MATLAB.

Optimization and Control Numerical Analysis Programming Languages

A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential operators and the one-dimensional ultraspherical spectral method.

Numerical Analysis

A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems.

Numerical Analysis

Polyak momentum (PM), also known as the heavy-ball method, is a widely used optimization method that enjoys an asymptotic optimal worst-case complexity on quadratic objectives.

Optimization and Control

We express both the numerical simulations and DNNs using computational graphs and therefore, we can calculate the gradients using reverse-mode automatic differentiation.

Numerical Analysis Numerical Analysis

One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces.

Numerical Analysis Numerical Analysis Computational Physics