Integrating equation solvers with probabilistic programming through differentiable programming


Part of the COMPUTATIONAL ABSTRACTIONS FOR PROBABILISTIC AND DIFFERENTIABLE PROGRAMMING WORKSHOP

Abstract: Many probabilistic programming languages (PPLs) attempt to integrate with equation solvers (differential equations, nonlinear equations, partial differential equations, etc.) from the inside, i.e. the developers of the PPLs like Stan provide differential equation solver choices as part of the suite. However, as equation solvers are an entire discipline to themselves with many active development communities and subfields, this places an immense burden on PPL developers to keep up with the changing landscape of tens of thousands of independent researchers. In this talk we will explore how Julia PPLs such as Turing.jl support of equation solvers from the outside, i.e. how the tools of differentiable programming allows equation solver libraries to be compatible with PPLs … READ MORE

How Inexact Models and Scientific Machine Learning Can Guide Decision Making in Quantitative Systems Pharmacology


Pre-clinical Quantitiative Systems Pharmacology (QSP) is about trying to understand how a drug target effects an outcome. If I effect this part of the biological pathways, how will it induce toxicity? Will it be effective?

Recently I have been pulling in a lot of technical collegues to help with the development of next generation QSP tooling. Without a background in biological modeling, I found it difficult to explain the "how" and "why" of pharmacological modeling. Why is it differential equations, and where do these "massively expensive global optimization" runs come from? What kinds of problems can you solve with such models when you know that they are only approximate?

To solve these questions, I took a step back and tried to explain a decision making scenario with a simple model, to showcase how playing with a model can allow one to distinguish … READ MORE

The Essential Tools of Scientific Machine Learning (Scientific ML)


Scientific machine learning is a burgeoning discipline which blends scientific computing and machine learning. Traditionally, scientific computing focuses on large-scale mechanistic models, usually differential equations, that are derived from scientific laws that simplified and explained phenomena. On the other hand, machine learning focuses on developing non-mechanistic data-driven models which require minimal knowledge and prior assumptions. The two sides have their pros and cons: differential equation models are great at extrapolating, the terms are explainable, and they can be fit with small data and few parameters. Machine learning models on the other hand require “big data” and lots of parameters but are not biased by the scientists ability to correctly identify valid laws and assumptions.

However, the recent trend has been to merge the two disciplines, allowing explainable models that are data-driven, require less data than traditional machine learning, and utilize the … READ MORE