Trending Research
PySINDy: A Python package for the Sparse Identification of Nonlinear Dynamics from Data
PySINDy is a Python package for the discovery of governing dynamical systems models from data.
Dynamical Systems Computational Physics
Optimizing a DIscrete Loss (ODIL) to solve forward and inverse problems for partial differential equations using machine learning tools
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
Large Sample Properties of Partitioning-Based Series Estimators
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
Optimal Routing for Constant Function Market Makers
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
Computing in Operations Research using Julia
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
The automatic solution of partial differential equations using a global spectral method
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
On symmetrizing the ultraspherical spectral method for self-adjoint problems
A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems.
Numerical Analysis
Universal Average-Case Optimality of Polyak Momentum
d2l-ai/d2l-en
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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
ADCME: Learning Spatially-varying Physical Fields using Deep Neural Networks
kailaix/ADCME.jl
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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
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces.
Numerical Analysis Numerical Analysis Computational Physics
