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Found 15 papers, 12 papers with code
Locally Regularized Neural Differential Equations: Some Black Boxes Were Meant to Remain Closed!
Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically.
Backpropagation through Back Substitution with a Backslash
This paper has three contributions: (i) it is of intellectual value to replace traditional treatments of automatic differentiation with a (left acting) operator theoretic, graph-based approach; (ii) operators can be readily placed in matrices in software in programming languages such as Julia as an implementation option; (iii) we introduce a novel notation, ``transpose dot'' operator ``$\{\}^{T_\bullet}$'' that allows for the reversal of operators.
Continuous Deep Equilibrium Models: Training Neural ODEs faster by integrating them to Infinity
Additionally, we address the question: is there a way to simultaneously achieve the robustness of implicit layers while allowing the reduced computational expense of an explicit layer?
High-performance symbolic-numerics via multiple dispatch
We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations.
AutoMat: Accelerated Computational Electrochemical systems Discovery
Large-scale electrification is vital to addressing the climate crisis, but several scientific and technological challenges remain to fully electrify both the chemical industry and transportation.
Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks
Modern design, control, and optimization often requires simulation of highly nonlinear models, leading to prohibitive computational costs.
Signal Enhancement for Magnetic Navigation Challenge Problem
It is difficult to separate the Earth magnetic anomaly field, which is crucial for navigation, from the total magnetic field reading from the sensor.
Universal Differential Equations for Scientific Machine Learning
In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets."
A Differentiable Programming System to Bridge Machine Learning and Scientific Computing
Scientific computing is increasingly incorporating the advancements in machine learning and the ability to work with large amounts of data.
Circuitscape in Julia: High Performance Connectivity Modelling to Support Conservation Decisions
Connectivity across landscapes influences a wide range of conservation-relevant ecological processes, including species movements, gene flow, and the spread of wildfire, pests, and diseases.
TabulaROSA: Tabular Operating System Architecture for Massively Parallel Heterogeneous Compute Engines
In this context, an operating system can be viewed as software that brokers and tracks the resources of the compute engines and is akin to a database management system.
Distributed, Parallel, and Cluster Computing Databases Operating Systems Performance
Accelerated Convolutions for Efficient Multi-Scale Time to Contact Computation in Julia
Efficient computation of convolutions is critical to artificial intelligence in real-time applications, like machine vision, where convolutions must be continuously and efficiently computed on tens to hundreds of kilobytes per second.
Julia: A Fresh Approach to Numerical Computing
Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing.
Mathematical Software
Julia: A Fast Dynamic Language for Technical Computing
Dynamic languages have become popular for scientific computing.
Programming Languages Computational Engineering, Finance, and Science D.3.2
Matrix Models for Beta Ensembles
This paper constructs tridiagonal random matrix models for general ($\beta>0$) $\beta$-Hermite (Gaussian) and $\beta$-Laguerre (Wishart) ensembles.
Mathematical Physics Mathematical Physics Probability Representation Theory
