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Sensitivity Analysis Explained: What Exactly Is It?

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26 Mar 2025

Table of Links

Abstract and 1. Introduction

2. Mathematical Description and 2.1. Numerical Algorithms for Nonlinear Equations

2.2. Globalization Strategies

2.3. Sensitivity Analysis

2.4. Matrix Coloring & Sparse Automatic Differentiation

3. Special Capabilities

3.1. Composable Building Blocks

3.2. Smart PolyAlgortihm Defaults

3.3. Non-Allocating Static Algorithms inside GPU Kernels

3.4. Automatic Sparsity Exploitation

3.5. Generalized Jacobian-Free Nonlinear Solvers using Krylov Methods

4. Results and 4.1. Robustness on 23 Test Problems

4.2. Initializing the Doyle-Fuller-Newman (DFN) Battery Model

4.3. Large Ill-Conditioned Nonlinear Brusselator System

5. Conclusion and References

This paper is available on arxiv under CC BY 4.0 DEED license.


[6] We defer the discussion on how to efficiently compute nonlinear solve adjoints for large systems to [9]

Authors:

(1) AVIK PAL, CSAIL MIT, Cambridge, MA;

(2) FLEMMING HOLTORF;

(3) AXEL LARSSON;

(4) TORKEL LOMAN;

(5) UTKARSH;

(6) FRANK SCHÄFER;

(7) QINGYU QU;

(8) ALAN EDELMAN;

(9) CHRIS RACKAUCKAS, CSAIL MIT, Cambridge, MA.


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