Advanced Numerics for Uncertainty and Bayesian Inference in Science

Introduction

Scientific knowledge enters computers through data on one side, and laws of nature – implicit equations like differential equations and symmetries – on the other. They both provide information, empirical and mechanistic, respectively, crucial to the deduction of new insights.

Challenges in Current Approaches

However, the algorithms that operate on these sources of information stem from different communities and different eras: machine learning – "big data" – on one hand, and simulation methods – high-performance computing – on the other.

Disconnect Issues

One of the problems that arise from this disconnect is that inferring latent forces that drive dynamical systems from data requires "shoehorning" different algorithms together in inefficient optimization loops. Another issue is that uncertainty from discretization and emulation is not fully tracked.

Emergence of Probabilistic Numerical Methods

Probabilistic numerical methods have emerged over the last decade as a holistic view on computation as inference. They provide a unifying language that can leverage empirical and mechanistic information.

Research Program Objectives

This proposal outlines a research program to complement and scale probabilistic numerical methods to enrich the quantitative scientist's toolbox along three axes:

1. Unifying Uncertainty: Unifying uncertainty from empirical and computational knowledge in one common formalism, which allows the direct and robust combination of simulation and experimentation.
2. Developing a Semantic Language: Developing a rich and practical semantic language for the description of different types of knowledge – mechanistic, empirical, practical.
3. Enhancing Computational Efficiency: Achieving significant computational efficiency gains by managing the computational process globally, instead of as a series of black boxes.

Practical Relevance and Implementation

Real scientific tasks will provide benchmarks and ensure practical relevance. An open-source software toolbox, complemented by regular summer schools, will ensure that the results reach their audience.

Conclusion

As a result, ANUBIS will start a genuinely novel kind of quantitative scientific analysis at the intersection of simulation and machine learning.