Johann Rudi

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a Bayesian inverse problem. We consider a parametrized system of nonlinear ordinary differential equations (ODEs), which is the FitzHugh--Nagumo model. The considered problem exhibits significant mathematical and computational challenges for classical parameter estimation methods, including strong nonlinearities, nonconvexity, and sharp gradients. We explore how NNs overcome these challenges by approximating reconstruction maps for parameter estimation from observational data. The considered data are time series of the spiking membrane potential of a biological neuron. We infer parameters controlling the dynamics of the model, noise parameters of autocorrelated additive noise, and noise modeled via stochastic differential equations, as well as the covariance matrix of the posterior distribution to expose parameter uncertainties--all with just one forward evaluation of an appropriate NN. We report results for different NN architectures and study the influence of noise on prediction accuracy. We also report timing results for training NNs on dedicated hardware. Our results demonstrate that NNs are a versatile tool to estimate parameters of the dynamical system, stochastic processes, as well as uncertainties, as they propagate through the governing ODE.

CG-Kit is a new code generation toolkit that we propose as a solution for portability and maintainability for scientific computing applications. The development of CG-Kit is rooted in the urgent need created by the shifting landscape of high-performance computing platforms and the algorithmic complexities of a particular large-scale multiphysics application: Flash-X. This combination leads to unique challenges including handling an existing large code base in Fortran and/or C/C++, subdivision of code into a great variety of units supporting a wide range of physics and numerical methods, different parallelization techniques for distributed- and shared-memory systems and accelerator devices, and heterogeneity of computing platforms requiring coexisting variants of parallel algorithms. The challenges demand that developers determine custom abstractions and granularity for code generation. CG-Kit tackles this with standalone tools that can be combined into highly specific and, we argue, highly effective portability and maintainability tool chains. Here we present the design of our new tools: parametrized source trees, control flow graphs, and recipes. The tools are implemented in Python. Although the tools are agnostic to the programming language of the source code, we focus on C/C++ and Fortran. Code generation experiments demonstrate the generation of variants of parallel algorithms: first, multithreaded variants of the basic AXPY operation (scalar-vector addition and vector-vector multiplication) to introduce the application of CG-Kit tool chains; and second, variants of parallel algorithms within a hydrodynamics solver, called Spark, from Flash-X that operates on block-structured adaptive meshes. In summary, code generated by CG-Kit achieves a reduction by over 60% of the original C/C++/Fortran source code.