Practicum Abstracts

Our first goal was to numerically resolve the oscillatory dynamics for a mechanistic model of yeast cell growth in a bioreactor using several high-order and physics-matched numerical flux discretization schemes. This involved adapting previous published work on a system of coupled hyperbolic partial- and ordinary differential equations with non-smooth function definitions that could be used to predict and control cell subpopulations in the production of yeast. Upon achieving a fast and efficient implementation of the forward solve and forward sensitivity equation generation, we then embedded the model as a dynamic constraint into a multi-objective optimal control formulation. The choice of control inputs to vary was practically motivated by real world operational limitations and the current state of process analytical technology (PAT). Moreover, the multi-objective was formulated with both an economic objective (to maximize profits) and a controller performance objective (to minimize system oscillations). We then solved the optimal control problem (OCP) by deploying a direct multiple shooting approach that reformulated the OCP as a finite dimensional, large-scale non-convex optimization problem that could be tackled using state-of-the-art derivative and derivative-free solvers. Finally, using the epsilon-constraint method, we concluded the project with repeated solutions of the OCP under different weighting of the individual objectives to map out the pareto surface and visualize the trade-offs possible in operating the yeast cell bioreactor.

Spin-defects in semiconductors, such as nitrogen-vacancy centers in diamond or divacancies in silicon carbide, are promising candidates for qubits, due to their optical controllability and relatively long coherence times. In most semiconductors, the hyperfine interaction of the central defect spin with isotopic nuclear spins is the main source of decoherence. Currently there are no automatic and efficient techniques for high-throughput characterization of local random nuclear spin baths in materials containing spin-defects, since direct experimental characterization is too time-consuming and labor-intensive for many samples. Although we can efficiently simulate dynamical decoupling experiments for a given configuration of nuclear spins, the inverse problem of recovering the hyperfine interactions from a relatively short dynamical decoupling experiment is ill-posed. Using simulated data, however, we can augment relatively short dynamical decoupling experiments to interpret the reliability and accuracy of hyperfine couplings extracted from these experiments. The set of tools we develop can be used to validate the mathematical and physical bounds on proposed sets of hyperfine couplings obtained from data-driven, machine-learned, or advanced sampling methods. These tools can be used to guide experimental design for dynamical decoupling protocols and pave the way for high-throughput characterization of defects in semiconductors.

In my second practicum experience, I worked on developing and implementing a modern, exascale-ready code for performing selected configuration interaction calculations, a particularly expensive ab-initio method in quantum chemistry and materials science which involves solving eigenvalue problems on extremely large matrices for which the entries are expensive to compute. An exascale-ready implementation is necessary for calculating extremely accurate properties of systems of interest, such as solids with transition metals or strongly correlated electrons.

I primarily worked on two projects during the summer. The first concerned non-thermalizing phases of matter---robust parameter regimes of a many-body quantum system in which the system fails to thermally equilibrate---and the latter concerned analog approaches to quantum error correction. To elaborate on the first, I worked with Ivar and his group members (in particular, Lei Su) to investigate a curious phenomenon we observed in the literature on non-thermalizing phases of matter. In particular, we observed that in many numerical studies, when two non-thermalizing phases were present in a phase diagram, a direct transition between such phases never occurred. Typically, transitions between such phases were interrupted by intervening thermalizing phases. We sought to understand this analytically in a concrete setting: transitions between symmetry-enriched non-ergodic phases of monitored quantum circuits. We approached this by trying to generalize statistical mechanics mappings typically used in studies of monitored quantum circuits to the case where the gate set and measurements respected some symmetry. We found that, while straightforward generalizations were impossible, if the gates were treated as the Kraus operators of a symmetric quantum channel, then it was possible to map the entanglement dynamics of the circuit to the finite temperature partition function of a gauge theory. It remains to be understood the phases of this gauge theory map encode the phases and phase transitions of the monitored quantum circuit. The difficulty lies in the fact that the gauge theory is not classical and understanding the finite-temperature phases of a quantum gauge theory is in general very challenging. To elaborate on the second, Ivar and I worked on the topic of quantum error correction. In particular, a quantum error correction protocol consists of picking some encoding logical information into a subspace of a many-body quantum Hilbert space and then engineering the dynamics of the system to get rid of errors that kick you out of the subspace. While the dynamics of the system are typically performed digitally (i.e. using unitary gates, projective measurements, and classical feedback), Ivar and I recognized that for some interesting quantum error correcting codes, these dynamics could be implemented in a local and analog way (i.e. using the native interactions between qubits and the natural decay of the qubits polarization). This could make these quantum error correcting protocols easier to realize in existing quantum technologies (e.g. dual species Rydberg atom arrays). Developing concrete experimental blueprints for these ideas remains to be done.

Machine learned interatomic potentials (MLIPs) are a hot topic in molecular dynamics because they can combine the accuracy of Ab initio calculations with the speed of classical force fields. It is not clear whether MLIPS can be applied to complex systems such as those including a sharp interface between two materials or phases, where interfacial polarization may occur. We aimed to study the applicability of machine learned forcefields to the air-water interface, and then further study the thermodynamics of ion adsorption at that interface. We collected training data using Ab initio molecular dynamics (AIMD) in CP2K, and trained accurate MLIPs using the NequIP software package. We verified our MLIPs by comparing directly to AIMD as well as previous literature.

I worked on a technique for mapping a large quantum circuit to a distributed quantum computing scenario. The technique involves formulating a quantum circuit as a graph, using a graph partitioning algorithm, and applying a post-processing procedure.

The Exa Power Flow team at Argonne is working on developing algorithms for solving AC optimal power flow problems—a class of non-convex optimization problems—on high-performance machines. The main challenge is taking state-of-the-art optimization algorithms, usually interior point methods, and porting them to GPU-based machine and distributed architectures. These algorithms parallelize poorly by default, so there is significant work to be done in adapting them to modern, highly parallel compute clusters.

Molecular dynamics requires the integration of an interatomic potential suitable for the system of interest. Unlike pair or two-body potentials, such as the Lennard-Jones (LJ) and Coulombic interactions, many-body potentials require complex expressions that sum over three or more atomic interactions. Despite the clear need for accurate and transferable many-body potentials, developing the necessary force fields requires prohibitively lengthy fitting and data generation procedures to obtain the desired accuracy. In this work, we deploy a symbolic regression framework to obtain the functional forms of, first, pair-wise interatomic potentials for a broad range of zeolite polymorphs. The framework implements a Monte Carlo Tree Search (MCTS) algorithm and uses a newly generated strongly constrained and appropriately normed (SCAN) method.

We focused on the SARS-CoV-2 virus, which causes COVID-19, the Severe Acute Respiratory Syndrome (SARS) at the root of the ongoing Pandemic since late 2019. We initiated the deployment of a machine learning-driven multiscale modeling framework to characterize the genomic evolution of SARS-CoV-2 .

The project was mainly focused on implementing a new method for calculating spectral densities for solid materials, a property which is important for understanding excited state behavior, into an established physics package. The implementation, while simple mathematically, required special attention to performance and HPC implementation in order to make problems of interest feasible to calculate; it is the first implementation of the method for solid materials.

Retrosynthetic pathway planning is the task of identifying a set of starting molecules and reactions that synthesize a desired destination molecule. The task is challenging because the space of possible reactions is combinatorial, making it too large for brute-force search. In this project, we investigated the use of reinforcement learning as a way to efficiently learn how to construct retrosynthesis pathways.

The project involved the development of compiler abstractions and transformations for parallel, specifically GPU, OpenMP, and MPI frameworks. Three separate projects were explored, at different times throughout the practicum. First, we explored how to efficiently optimize and differentiate GPU kernels. This involved emitting code to reason about races, efficiently use multiple levels of memory, developing AD-specific and GPU-specific optimizations, and creating abstractions to allow the compiler to emit GPU math functions. We then explored how this approach could be extended to efficiently differentiate and optimize OpenMP and MPI codes, as well as programs that use a combination of the aforementioned tools. Finally, we have begun exploring efficient representations of GPU barriers to enable development of a tool for creating fast and legal CPU code from existing GPU kernels.

The SARS-CoV-2 replication-transcription complex (RTC) is a multi-protein structure composed of nonstructural proteins (NSPs) which together are involved in the process of reproducing the viral genome. This complex plays an important role in the viral life cycle, and is therefore an important drug target. Understanding the atomistic details of this complex is essential for understanding the RNA processing. We have been combining AI and molecular dynamics, as well as FFEA to be able to improve our ability to use experimental data such as structures provided by Cryo-EM experiments.

Large, nonconvex, and nonlinear problems arise naturally in physical inverse problems and machine learning applications. Examples of these are the nonsmooth regularization of generalized lasso, low-rank regularized matrix completion, sparse convolutional neural networks, and physics-based, PDE-constrained optimization. This practicum will focus on developing a novel method for problems with these characteristics and then explore the descent and convergence properties of this algorithm in the context of the aforementioned settings. In typical inverse problems, one minimizes some cost/data misfit function to find model parameters that effectively capture the collected data. The issue is that cost functions for physics and machine learning applications are challenging for many standard minimization algorithms, which make often convexity and smoothness assumptions about the problem. While progress has been made in adapting existing algorithms to these difficult settings, the issues of computational cost and convergence guarantees still remain. One such promising algorithm is Alternating Direction Method of Multipliers (ADMM). ADMM is one of the workhorses for many machine learning and common optimization settings, and is considered a useful alternative to stochastic gradient descent (SGD) in nonlinear and nonconvex realms with large computational cost. It primarily functions by splitting up a difficult cost function in simpler parts, and solving these simpler problems iteratively until some sort of convergence is achieved. However, most nonconvex and nonlinear problems still lack global convergence guarantees and tend to converge slowly even towards local minima. Hence, solutions given by ADMM and SGD can come burdened with a lot of uncertainty. In addition, slow convergence to even local minima increases the computational cost of implementing these algorithms, as increased iterations of an already expensive model run burden these techniques. At ANL, we plan to study these issues through the lens of filter methods for ADMM. Filter methods have proved particularly promising for enforcing convergence in nonlinear programs. They have been shown to increase performance for sequential quadratic programs and interior point methods, as well as provide first order convergence guarantees for a variety of function types and constraints. The goal of this practicum is to develop an ADMM filter method for highly nonlinear and nonconvex problems, and then implementing this method numerically on sparsity-enforcing cost functions (ie p-norms for 0