Efficient implicit solvers for models of neuronal networks

We introduce economical versions of standard implicit ODE solvers that are specifically tailored for the efficient and accurate simulation of neural networks. The specific versions of the ODE solvers proposed here, allow to achieve a significant increase in the efficiency of network simulations, by reducing the size of the algebraic system being solved at each time step, a technique inspired by very successful semi-implicit approaches in computational fluid dynamics and structural mechanics. While we focus here specifically on Explicit first step, Diagonally Implicit Runge Kutta methods (ESDIRK), similar simplifications can also be applied to any implicit ODE solver. In order to demonstrate the capabilities of the proposed methods, we consider networks based on three different single cell models with slow-fast dynamics, including the classical FitzHugh-Nagumo model, a Intracellular Calcium Concentration model and the Hindmarsh-Rose model. Numerical experiments on the simulation of networks of increasing size based on these models demonstrate the increased efficiency of the proposed methods

A Comparative Study of Sensitivity Computations in ESDIRK-Based Optimal Control Problems

In this paper, we compare the impact of iterated and direct approaches to sensitivity computation in fixed-step explicit singly diagonally-implicit Runge-Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We use the principle of internal numerical differentiation (IND) strictly for the iterated approach, i.e., reusing the iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of the iterated and direct sensitivity computations in OCPs for the quadruple tank system. We benchmark the iterated and direct approaches with a base case. This base case is an OCP that applies an ESDIRK method that refactorizes the iteration matrix in every Newton iteration and uses a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and we evaluate the performance based on the number of SQP and QPs iterations, KKT violations, and the total number of function evaluations, Jacobian updates, and iteration matrix factorizations. The results indicate that the iterated approach outperforms the direct approach but yields similar performance to the base case.Comment: 6 pages, 5 figures, 2 tables. Submitted for European Control Conference 2024 (ECC2024). Stockholm, Swede

Experimental Investigation and High Resolution Simulation of In-Situ Combustion Processes

This final technical report describes work performed for the project 'Experimental Investigation and High Resolution Numerical Simulator of In-Situ Combustion Processes', DE-FC26-03NT15405. In summary, this work improved our understanding of in-situ combustion (ISC) process physics and oil recovery. This understanding was translated into improved conceptual models and a suite of software algorithms that extended predictive capabilities. We pursued experimental, theoretical, and numerical tasks during the performance period. The specific project objectives were (i) identification, experimentally, of chemical additives/injectants that improve combustion performance and delineation of the physics of improved performance, (ii) establishment of a benchmark one-dimensional, experimental data set for verification of in-situ combustion dynamics computed by simulators, (iii) develop improved numerical methods that can be used to describe in-situ combustion more accurately, and (iv) to lay the underpinnings of a highly efficient, 3D, in-situ combustion simulator using adaptive mesh refinement techniques and parallelization. We believe that project goals were met and exceeded as discussed