Optimizing the Future: Argonne at AN25

Researchers from the U.S. Department of Energy’s Argonne National Laboratory’s Mathematics and Computer Science division shared cutting-edge developments in large-scale numerical optimization at The Third Joint SIAM/CAIMS Annual Meetings (AN25), held July 28–Aug. 1, 2025, in Montréal, Canada. The event, co-sponsored by the Society for Industrial and Applied Mathematics (SIAM) and the Canadian Applied and Industrial Mathematics Society (CAIMS), gathered experts to explore the latest in applied mathematics, computational science and data science applications.

Highlights from Argonne’s Presentations

Tackling Massive Combinatorial Challenges
Sven Leyffer gave the Past President’s Address, in which he discussed solving mixed-integer PDE-constrained optimization (MIPDECO) problems — once considered infeasible because of their scale and complexity. He demonstrated how two new methods make solving certain MIPDECOs tractable, particularly in topology optimization. 

Modeling Fine-Scale Dynamics Efficiently
Emil Constantinescu showed how neural ordinary differential equations can be embedded into PDE formulations using the method of lines and conservation laws. This integration reduces computational cost while preserving accuracy, advancing operator learning at the intersection of numerical analysis and machine learning.

Optimizing Quantum Information Processing
Jeff Larson organized the mini symposium ​“Methods and Models for Numerical Optimization in Quantum Information Sciences,” where he also presented his work on bivariate bicycle codes. These codes protect quantum data from errors, but their optimal placement poses a massive search problem. Larson proposed a mixed-integer optimization model to narrow the search space and invited the broader community to help tackle this open challenge.

Quantifying Quantum Precision
Matt Menickelly explored how the quantum Fisher information sets limits on the precision of parameter estimates in quantum states. The information is crucial for determining the sensitivity of quantum sensors to parameter changes. He shared both successful strategies and challenges in applying structure-exploiting optimization methods to improve quantum sensing.

Recovering Incomplete Signal Data
Vishwas Rao addressed the problem of recovering sparse discrete Fourier transforms from noisy or incomplete signals — key in applications like GPS and medical imaging. He reformulated the problem using GPU-accelerated interior point and Krylov methods, along with fast Fourier transform toolkits and preconditioners. His approach scales to problems with hundreds of millions of variables and helps reduce artifacts in X-ray crystallography analysis.

Balancing Research and Professional Service
In a careers panel, Sven Leyffer gave a talk titled ​“Assimilation by the SIAM Collective: How to Engage SIAM and Be Engaged by SIAM,” reflecting on the interplay between professional service and an active research career.

Computing Sparse Derivative Matrices Efficiently
At the Applied and Computational Discrete Algorithms conference, co-located with AN25, Paul Hovland gave a talk on how to reduce the number of bit probes when determining Jacobian and Hessian sparsity patterns. His solution is to combine Bayesian probing and Bloom filter probing to overcome the shortcomings of each method in isolation.