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Found 12 papers, 9 papers with code
Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraints
Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant limitations.
Differentiable Programming for Differential Equations: A Review
Many scientific models are based on differential equations, where differentiable programming plays a crucial role in calculating model sensitivities, inverting model parameters, and training hybrid models that combine differential equations with data-driven approaches.
Differentiating Metropolis-Hastings to Optimize Intractable Densities
We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers, allowing us to differentiate through probabilistic inference, even if the model has discrete components within it.
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?
Julia for Biologists
Increasing emphasis on data and quantitative methods in the biomedical sciences is making biological research more computational.
Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristics
While we can control the computational cost by choosing the number of layers in standard architectures, in NDEs the number of neural network evaluations for a forward pass can depend on the number of steps of the adaptive ODE solver.
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.
Stiff Neural Ordinary Differential Equations
We first show the challenges of learning neural ODE in the classical stiff ODE systems of Robertson's problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems.
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.
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 Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions
In this manuscript we investigate the performance characteristics of Discrete Local Sensitivity Analysis implemented via Automatic Differentiation (DSAAD) against continuous adjoint sensitivity analysis.
Numerical Analysis
Confederated Modular Differential Equation APIs for Accelerated Algorithm Development and Benchmarking
Performant numerical solving of differential equations is required for large-scale scientific modeling.
Software Engineering Mathematical Software
