Embark on a captivating journey through the evolution of computational science in this keynote address from JuliaCon 2020. Prof Linda Petzold shares her extensive experience, from programming with punch cards to developing sophisticated algorithms for differential equations. Explore the challenges and breakthroughs in solving Ordinary Differential Equations (ODEs) and Differential-Algebraic Equations (DAEs), including the development of LSODA and DASKR. Discover applications in various fields such as computational combustion, solar power, spacecraft trajectories, and chemical vapor deposition. Delve into discrete stochastic simulations and their relevance in biological systems, including circadian rhythms and COVID-19 modeling. The talk concludes with a Q&A session addressing software engineering challenges in scientific computing, modeling biological systems, and the intersection of differential equations and machine learning.
Adventures in Computing - From Punch Cards to Differential Equations
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Overview
Syllabus
Welcome!.
Programming with punch cards.
My first serious encounter with numerical methods for ODEs.
Why should users have to decide whether their problem is stiff or not?.
Livermore Solver for Ordinary Differential Equations Automatic (LSODA) is now available in Julia by LSODA.jl.
Computational combustion (see DASSL.jl) and lessons about releasing code.
Solar power plan and challenges that it provided.
True problem wasn't in the code but in our math.
"DAEs are not ODEs" (Differential-Algebraic Equations).
Development of theory and algorithms for Differential-Algebraic Equations (DAE, see DASKR.jl).
Solving F = ma with constraints.
DAEs and various problems on which I was working around 1991.
DAEs and parameter estimations, optimal control, etc..
Working on trajectories of small spacecraft.
Chemical vapor deposition and DAE.
Discrete stochastic simulations.
Stochasticity in biological systems.
Circadian rhythm.
Spatial stochastic simulation.
Stochastic simulation of COVID-19.
Acknowledgments.
Q&A: What do you think about barriers that scientists encounter when dealing with software engineering?.
Q&A: What are your reflections on modeling biological systems?.
Q&A: What do you think about the recent hype that differential equations get from the machine learning community?.
Taught by
The Julia Programming Language
