ABSTRACT: Based on the Kolmogorov-Arnold network (KAN), we present a novel emulator of the global 21 cm cosmology signal, 21cmKAN, that provides extremely fast training speed while achieving nearly equivalent accuracy to the most accurate emulator to date, 21cmLSTM. The combination of enhanced speed and accuracy facilitated by 21cmKAN enables rapid and highly accurate physical parameter estimation analyses of multiple 21 cm models, which is needed to fully characterize the complex feature space across models and produce robust constraints on the early Universe. Rather than using static functions to model complex relationships like traditional fully connected neural networks do, KANs learn expressive transformations that can perform significantly better for low-dimensional physical problems. 21cmKAN predicts a given signal for two well-known models in the community in 3.7 ms on average and trains about 75 times faster than 21cmLSTM, when utilizing the same typical GPU. In addition, 21cmKAN is able to achieve these speeds because of its learnable, data-driven transformations and its relatively small number of trainable parameters compared to a memory-based emulator. We show that 21cmKAN required less than 30 minutes to train and fit these simulated signals and obtain unbiased posterior distributions. We find that the transparent architecture of 21cmKAN allows us to conveniently interpret and further validate its emulation results in terms of the sensitivity of the 21 cm signal to each physical parameter. This work demonstrates the effectiveness of KANs and their ability to more quickly and accurately mimic expensive physical simulations in comparison to other types of neural networks.

ABSTRACT: As demand for computational power grows, access to advanced cyberinfrastructure (CI) and the professionals needed to support it has become increasingly critical. However, hiring and retaining cyberinfrastructure professionals (CIPs) remains a significant challenge, as many trained in enterprise services lack the specialized skills required for advanced CI administration. To address this gap, a student cohort program was implemented via the Rocky Mountain Advanced Computing Consortium (RMACC), providing hands-on training in CI administration. The program included weekly virtual sessions, mentorship, and two in-person experiences where students participated in real-world system deployment and decommissioning tasks. Students gained practical experience in Slurm configuration, Linux proficiency, hardware procurement, and system troubleshooting. This initiative has proven highly successful, offering professional development opportunities and expanding the pipeline of skilled CIPs. The results emphasize the importance of integrating CI administration education into research computing programs to ensure the sustainability and growth of advanced CI support.

ABSTRACT: Computationally quantifying uncertainties in the mathematical modeling of physical processes is crucial for understanding the errors induced by both numerical approximations of the model and lack of precise input data assumed in the continuous model. Uncertain input parameters in the continuous model are typically treated as random variables, leading to the need to consider solutions of both the continuous and discrete models as stochastic processes. Computing statistical moments of the stochastic processes is an extremely important part of the uncertainty quantification problem. In this work, we consider a class of physical processes that are modeled by the Allen-Cahn (A-C) partial differential equation (PDE) evolutionary system, with uncertainties in the initial state of the evolution and the A-C PDE. We develop a hybrid computational model for the stochastic A-C system to efficiently compute statistical moments of the numerical counterparts of the A-C stochastic processes. The hybrid framework comprises finite element method in-space approximations, high-order digital nets based sampling in high dimensional probability space, and an interplay of discretization parameters in the spatial and stochastic approximations. We demonstrate marked efficiency of the hybrid framework, compared to the standard methods, using two- and three-dimensional in space and high stochastic dimensional A-C example systems.

ABSTRACT:

Background
Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws.

Results
In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability.

Conclusions
We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

ABSTRACT: We present a formulation of the physics-informed neural network (PINN) method for learning the effective viscosity of the generalized Newtonian fluid from measurements of velocity and pressure in time-dependent three-dimensional flows and apply it to estimating viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) in shear flow between two parallel plates using only velocity measurements from numerical simulations. The PINN-inferred viscosity models agree with empirical models for shear rates with large absolute values but deviate for shear rates near zero where empirical models have an unphysical singularity. We show that once the unknown physics is learned the PINN method can be used to solve the momentum conservation equation governing flow of non-Newtonian fluids.

ABSTRACT:

Motivation
Signaling pathways capable of switching between two states are ubiquitous within living organisms. They provide the cells with the means to produce reversible or irreversible decisions. Switch-like behavior of biological systems is realized through biochemical reaction networks capable of having two or more distinct steady states, which are dependent on initial conditions. Investigation of whether a certain signaling pathway can confer bistability involves a substantial amount of hypothesis testing. The cost of direct experimental testing can be prohibitive. Therefore, constraining the hypothesis space is highly beneficial. One such methodology is based on chemical reaction network theory (CRNT), which uses computational techniques to rule out pathways that are not capable of bistability regardless of kinetic constant values and molecule concentrations. Although useful, these methods are complicated from both pure and computational mathematics perspectives. Thus, their adoption is very limited amongst biologists.

Results
We brought CRNT approaches closer to experimental biologists by automating all the necessary steps in CRNT4SMBL. The input is based on systems biology markup language (SBML) format, which is the community standard for biological pathway communication. The tool parses SBML and derives C-graph representations of the biological pathway with mass action kinetics. Next steps involve an efficient search for potential saddle-node bifurcation points using an optimization technique. This type of bifurcation is important as it has the potential of acting as a switching point between two steady states. Finally, if any bifurcation points are present, continuation analysis with respect to a user-defined parameter extends the steady state branches and generates a bifurcation diagram. Presence of an S-shaped bifurcation diagram indicates that the pathway acts as a bistable switch for the given optimization parameters.

ABSTRACT: We consider a moving shutter and non-deterministic generalization of the diffraction in time model introduced by Moshinsky several decades ago to study a class of quantum transients. We first develop a moving-mesh finite element method (FEM) to simulate the determisitic version of the model. We then apply the FEM and multilevel Monte Carlo (MLMC) algorithm to the stochastic moving-domain model for simulation of approximate statistical moments of the density profile of the stochastic transients.