Automated shaker placement and regularized input estimation for MIMO testing
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Coletti, Keaton Patrick [Sandia National Laborator↗
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Optimization of Total Variation-Regularized Problems using Inexact Proximal Solves
Inexact proximal framework for total-variation minimization.
Kouri, Drew Philip [Sandia National Laboratories (↗
MINLP for regularized symbolic regression with applications to data-driven modeling of critical minerals processes
The poster summarizes recent advances in symbolic regression developed as part of the PrOMMiS project over the past year. In particular, it describes the comparison of surrogates for critical minerals (CM) & rare earth element (REE) recovery flowsheets obtained via symbolic regression and ALAMO. It also compares the predictive ability and solvability of optimization models that incorporate these surrogates.
36 MATERIALS SCIENCE↗
An Adaptive Inexact Trust-Region Method for PDE-Constrained Optimization with Regularized Objectives
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Baraldi, Robert John [Sandia National Laboratories↗
Automated shaker placement and regularized input estimation for MIMO testing
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Coletti, Keaton Patrick [Sandia National Laborator↗
A Particle Method for the Multispecies Landau Equation
Abstract The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method (Carrillo et al. in J. Comput. Phys. 7:100066, 2020) has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies Bobylev-Krook-Wu (BKW) solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples.
Mathematics↗
A chemical kinetic analysis of knock propensity of methanol-to-gasoline fuel
Production of low carbon gasoline-like fuels such as methanol-to-gasoline (MTG) is a promising approach to achieve rapid greenhouse gas emission reduction of the transportation sector. Despite the fact that gasoline that meets the ASTM D4814 standard for automotive spark-ignition engine fuel can be readily produced from these processes, it is unclear how the composition of MTG may affect engine performance and emissions. Here, in this paper, a surrogate for an MTG is used to numerically study the effects of gasoline composition on knock propensity and on the sensitivity of knock to thermal and fuel stratification, to oxygen dilution and to nitric oxide from exhaust gas recirculation of residual gases. Simulations were performed in ANSYS CHEMKIN-PRO using a comprehensive chemical kinetic mechanism for gasoline surrogates, and results of the MTG surrogate were compared against those of a petroleum-based regular E10 gasoline, termed PACE-20. A premium-grade MTG fuel was also formulated by adding ethanol to the MTG surrogate, and results were compared against those of four premium-grade, gasoline-like fuels representative of future alternative gasoline formulations. Surrogates and mechanism were evaluated by comparison against experimental engine data, and the model showed high accuracy at stoichiometric conditions (mean absolute error of ignition timing equal to 1.46 crank angle degrees) but larger deviations at lean conditions (mean absolute error of ignition timing equal to 5.52 crank angle degrees). Despite the fact that the MTG surrogate has a RON 1.1 units higher than that of PACE-20, it may show higher knock propensity at medium temperature conditions due to a less intense NTC behavior. MTG autoignition was more temperature- and equivalence ratio-sensitive than that of PACE20, suggesting that MTG can benefit more from naturally-occurring thermal stratification or from induced fuel stratification of the end gas to mitigate knock intensity. The sensitivity of autoignition reactivity to oxygen dilution and to NO concentration was higher for MTG than for regular gasoline at medium loads, but the opposite trend was observed at high loads due to the effect of pressure on the low-temperature chemistry of regular gasoline. Approximately 14 % vol ethanol content was required to upgrade the octane rating of MTG from regular grade to premium grade. Adding 13.6 % vol ethanol made the fuel autoignition less sensitive to both oxygen dilution and NO content (ignition time varies approx. 17 % and 50 % less with oxygen dilution and NO addition, respectively, when adding ethanol at high engine loads).
02 PETROLEUM↗
Repartitioning the Hamiltonian in many-body second-order Brillouin–Wigner perturbation theory: Uncovering new size-consistent models
Second-order Møller-Plesset perturbation theory is well-known as a computationally inexpensive approach to the electron correlation problem that is size-consistent with a size-consistent reference but fails to be regular. On the other hand, the less well-known many-body version of Brillouin-Wigner perturbation theory has the reverse properties: it is regular but fails to be size-consistent when used with the standard MP partitioning. Consequently, its widespread use remains limited. In this work, we analyze the ways in which it is possible to use alternative non-MP partitions of the Hamiltonian to yield variants of BW2 that are size-consistent as well as regular. We show that there is a vast space of such BW2 theories and also show that it is possible to define a repartitioned BW2 theory from the ground state density alone, which regenerates the exact correlation energy. We also provide a general recipe for deriving regular, size-consistent, and size-extensive partitions from physically meaningful components, and we apply the result to small model systems. The scope of these results appears to further set the stage for a revival of BW2 in quantum chemistry.
Ab initio perturbation↗
An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture
This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.
42 ENGINEERING↗
The approximate second order coupled-cluster method based on a size-consistent Brillouin–Wigner partitioning
We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin–Wigner (BW-s) partitioning instead of a Møller–Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree–Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. Furthermore, the main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.
Correlation energy↗
Improved Guarantees for Optimal Nash Equilibrium Seeking and Bilevel Variational Inequalities
We consider a class of hierarchical variational inequality (VI) problems that subsumes VI-constrained optimization and several other problem classes, including the optimal solution selection problem and the optimal Nash equilibrium (NE) seeking problem. Our main contribution is threefold. (i) We consider bilevel VIs with monotone and Lipschitz continuous mappings and devise a single-timescale iteratively regularized extragradient method, named IR-EG 𝚖,𝚖 . We improve the existing iteration complexity results for addressing both bilevel VI and VI-constrained convex optimization problems. (ii) Under the strong monotonicity of the outer-level mapping, we develop a method named IR-EG 𝚜,𝚖 and derive faster guarantees than those in (i). We also study the iteration complexity of this method under a constant regularization parameter. These results appear to be new for both bilevel VIs and VI-constrained optimization. (iii) To our knowledge, complexity guarantees for computing the optimal NE in nonconvex settings do not exist. Motivated by this lacuna, we consider VI-constrained nonconvex optimization problems and devise an inexactly projected gradient method, named IPR-EG, where the projection onto the unknown set of equilibria is performed using IR-EG 𝚜,𝚖 with a prescribed termination criterion and an adaptive regularization parameter. We obtain new complexity guarantees in terms of a residual map and an infeasibility metric for computing a stationary point. Here, we validate the theoretical findings using preliminary numerical experiments for computing the best and the worst NEs.
bilevel optimization↗
Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes
We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.
97 MATHEMATICS AND COMPUTING↗
A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints
Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.
PDE-constrained optimization↗
NuGraph2 with context-aware inputs: physics-inspired improvements in semantic segmentation
Graph neural networks have recently shown strong promise for event reconstruction tasks in Liquid Argon Time Projection Chambers, yet their performance remains limited for underrepresented classes of particles, such as Michel electrons. In this work, we investigate physics-informed strategies to improve semantic segmentation within the NuGraph2 architecture. We explore three complementary approaches: (i) enriching the input representation with context-aware features derived from detector geometry and track continuity, (ii) introducing auxiliary decoders to capture class-level correlations, and (iii) incorporating energy-based regularization terms motivated by Michel electron energy distributions. Experiments on MicroBooNE public datasets show that physics-inspired feature augmentation yields the largest gains, particularly boosting Michel electron precision and recall by disentangling overlapping latent space regions. In contrast, auxiliary decoders and energy-regularization terms provided limited improvements, partly due to the hit-level nature of NuGraph2, which lacks explicit particle- or event-level representations. Our findings highlight that embedding physics context directly into node-level inputs is more effective than imposing task-specific auxiliary losses, and suggest that future hierarchical architectures such as NuGraph3, with explicit particle- and event-level reasoning, will provide a more natural setting for advanced decoders and physics-based regularization. The code for this work is publicly available on Github at https://github.com/vitorgrizzi/nugraph_phys/tree/main_phys.
Other Experiments↗
High compressive energy absorption and shape recovery behavior of additively manufactured textile-inspired cylindrical braided metamaterials
Mechanical metamaterials (MMs) are engineered structures with unique mechanical properties that arise from their unique spatial arrangement or lattice-like structure. The most commonly designed MMs such as honeycomb and re-entrant auxetics are prone to failure at the sharp corners and weak joints due to the increased stress concentration under deformation. To mitigate this challenge, braided MM structures involving intertwining threads of nylon—forming curved unit cells—have been studied. These textile-inspired cylindrical braided metamaterials (CBMMs) with contrasting unit cells, namely diamond and regular CBMMs, were fabricated by 3D printing. The layer-by-layer deposited structure built by fused filament fabrication delivered an assembly of overlapped threads that are fused at the contact point. To understand deformation behavior of these MMs, finite element models were developed for various load scenarios including quasi-static compression, cyclic and creep loads at room temperature. Stress distribution, deformation mechanisms, and failure modes were analyzed and validated by experiments to analyze the geometries and associated performance. The diamond CBMMs showed stress softening at 30 % compressive strain, withstanding a load of ∼440 N, whereas the regular CBMMs at 50 % strain experienced ∼250 N. The diamond CBMMs delivered higher creep resistance under sustained load and better energy absorption under cyclic loading than the regular CBMMs. The latter, however, exhibited 94 % shape recovery in contrast to 88 % recovery in former prototype during their first cyclic load. In conclusion, this study helps design mechanical lightweight devices that endure significant sustained load and exhibit enhanced energy absorption and shape recovery characteristics in cyclic loading.
Creep↗
A robust spectral element implementation of the $k - τ$ RANS model in Nek5000/NekRS
The $k - ω$ Reynolds Averaged Navier Stokes (RANS) model is one of the industry standard approaches for modeling of turbulent flows. It performs better than the $k - ϵ$ model for low Reynolds number flows and is also more suitable for boundary layers with adverse pressure gradients. Major drawback of the model, however, is that the asymptotic value of $ω$ at the walls is singular, necessitating the use of a contrived “sufficiently” large value for $ω$ as the boundary condition for its transport equation. Here, this invariably leads to the solution being sensitive to near wall grid spacing. While an acceptable solution for low order (finite volume) methods, the excessive near wall gradients lead to persistent numerical stability issues in high order codes. To alleviate the problem, specifically in the context of the high order spectral element code Nek5000, a regularized $k - ω$ approach was formulated in our prior work (Tomboulides et al., 2018). The formulation, however, relies on the use of wall distance and its gradients for modeling the closure terms and can pose problems for simulations in complex geometries. This work presents a novel implementation of the $k - τ$ RANS model in Nek5000, where $τ = 1/ω$, eliminating the need for regularization, owing to the asymptotically bounded behavior of the source terms in the $τ$ transport equation, and also eliminating dependence on wall distance. Robustness and stability of the $k - τ$ model is ensured through implicit treatment of the source terms and their careful numerical implementation and demonstrated through several cases aimed at verification and validation. Studies include both canonical and engineering relevant problems, viz., turbulent channel flow, pipe flow, backward facing step, flow over NACA 0012 airfoil and flow in a T-junction. Results from the $k - τ$ model are shown to be consistent with regularized $k - ω$ model and also with the $k - ω$ SST model in OpenFOAM (for select studies). Comparison with experimental data is also shown, where available, to bolster validation efforts for the $k - τ$ model implementation through prediction of key turbulent quantities of interest.
Nek5000↗
An extension of the localized artificial diffusivity method for immiscible and high density ratio flows
The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.
Artificial diffusivity↗
Space‐Time Causal Discovery in Earth System Science: A Local Stencil Learning Approach
Causal discovery tools enable scientists to infer meaningful relationships from observational data, spurring advances in fields as diverse as biology, economics, and climate science. Despite these successes, the application of causal discovery to space-time systems remains immensely challenging due to the high-dimensional nature of the data. For example, in climate sciences, modern observational temperature records over the past few decades regularly measure thousands of locations around the globe. To address these challenges, we introduce Causal Space-Time Stencil Learning (CaStLe), a novel meta-algorithm for discovering causal structures in complex space-time systems. CaStLe leverages regularities in local space-time dependencies to learn governing global dynamics. This local perspective eliminates spurious confounding and drastically reduces sample complexity, making space-time causal discovery practical and effective. For causal discovery, CaStLe flexibly accepts any appropriately adapted time series causal discovery algorithm to recover local causal structures. These advances enable causal discovery of geophysical phenomena that were previously unapproachable, including non-periodic, transient phenomena such as volcanic eruption plumes. Regularities in local space-time dependencies are transformed into informative spatial replicates, which actually improve CaStLe's performance when applied to ever-larger spatial grids. We successfully apply CaStLe to discover the atmospheric dynamics governing the climate response to the 1991 Mount Pinatubo volcanic eruption. We provide validation experiments to demonstrate the effectiveness of CaStLe over existing causal-discovery frameworks on a range of geophysics-inspired benchmarks while identifying the method's limitations and domains where its assumptions may not hold.
Nichol, J. Jake [Univ. of New Mexico, Albuquerque,↗