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DOE OSTI2022

Posterior Regularized Bayesian Neural Network incorporating soft and hard knowledge constraints

Neural Networks (NNs) have been widely used in supervised learning due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. Furthermore, the experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.

14 SOLAR ENERGY↗

DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗

DOE OSTI2025

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗

DOE OSTI2021

Regio‐Regular Polymer Acceptors Enabled by Determined Fluorination on End Groups for All‐Polymer Solar Cells with 15.2 % Efficiency

Abstract Polymerization sites of small molecule acceptors (SMAs) play vital roles in determining device performance of all‐polymer solar cells (all‐PSCs). Different from our recent work about fluoro‐ and bromo‐ co‐modified end group of IC‐FBr (a mixture of IC‐FBr1 and IC‐FBr2), in this paper, we synthesized and purified two regiospecific fluoro‐ and bromo‐ substituted end groups (IC‐FBr‐ o & IC‐FBr‐ m ), which were then employed to construct two regio‐regular polymer acceptors named PYF‐T‐ o and PYF‐T‐ m , respectively . In comparison with its isomeric counterparts named PYF‐T‐ m with different conjugated coupling sites, PYF‐T‐ o exhibits stronger and bathochromic absorption to achieve better photon harvesting. Meanwhile, PYF‐T‐ o adopts more ordered inter‐chain packing and suitable phase separation after blending with the donor polymer PM6, which resulted in suppressed charge recombination and efficient charge transport. Strikingly, we observed a dramatic performance difference between the two isomeric polymer acceptors PYF‐T‐ o and PYF‐T‐ m . While devices based on PM6:PYF‐T‐ o can yield power conversion efficiency (PCE) of 15.2 %, devices based on PM6:PYF‐T‐ m only show poor efficiencies of 1.4 %. This work demonstrates the success of configuration‐unique fluorinated end groups in designing high‐performance regular polymer acceptors, which provides guidelines towards developing all‐PSCs with better efficiencies.

Yu, Han↗

DOE OSTI2021

Regio‐Regular Polymer Acceptors Enabled by Determined Fluorination on End Groups for All‐Polymer Solar Cells with 15.2 % Efficiency

Yu, Han↗

DOE OSTI2023

High dimensional binary classification under label shift: phase transition and regularization

Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. Here, to bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that there exists a phase transition phenomenon: Under certain overparametrized regime, the classifier trained using imbalanced data outperforms the counterpart with reduced balanced data. Moreover, we investigate the impact of regularization to the label shift: The aforementioned phase transition vanishes as the regularization becomes strong.

binary classification↗

DOE OSTI2022

Nonconvex regularization for sparse neural networks

Convex ℓ 1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in this paper, a nonconvex regularization method is investigated in the context of shallow ReLU networks: We prove that in contrast to the convex approach, any resulting (locally optimal) network is finite even in the presence of infinite data (i.e., if the data distribution is known and the limiting case of infinite samples is considered). Moreover, here we show that approximation guarantees and existing bounds on the network size for finite data are maintained.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

From Anderson localization on random regular graphs to many-body localization

Highlights: • Anderson transition from ergodicity to localization on random regular graphs (RRG). • Analytical, pool method, and exact-diagonalization study of correlations on RRG. • Many-body localization (MBL) to ergodicity transition: quantum dots and spin chains. • Dynamical eigenstate correlation functions in RRG and MBL problems. • Anderson localization on RRG as a toy model for MBL. The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in delocalized and localized phases, as well at criticality, are discussed. In the many-body part, models with short-range and power-law interactions are considered, as well as the quantum-dot model representing the limit of the “most long-range” interaction. Central themes – which are common to the RRG and MBL problems – include ergodicity of the delocalized phase, localized character of the critical point, strong finite-size effects, and fractal scaling of eigenstate correlations in the localized phase.

36 MATERIALS SCIENCE↗

DOE OSTI2023

GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning

This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape of a scatterer, either in the context of material design or sensing, plays a critical role in many practical engineering problems. This class of inverse problems is extremely challenging due to their high-dimensional, nonlinear, and ill-posed nature. To overcome these technical hurdles, we introduce a geometric regularization approach for deep neural networks (DNN) based on non-uniform rational B-splines (NURBS) and capable of predicting complex 2D scatterer geometries in a parsimonious dimensional representation. Then, this geometric regularization is combined with physics-embedded learning and integrated within a robust convolutional autoencoder (CAE) architecture to accurately predict the shape of 2D scatterers in the context of identification and inverse design problems. Further, an extensive numerical study is presented in order to showcase the remarkable ability of this approach to handle complex scatterer geometries while generating physically-consistent acoustic fields. The study also assesses and contrasts the role played by the (weakly) embedded physics in the convergence of the DNN predictions to a physically consistent inverse design.

42 ENGINEERING↗

DOE OSTI2021

A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Long–short-term memory encoder–decoder with regularized hidden dynamics for fault detection in industrial processes

The ability of recurrent neural networks (RNN) to model nonlinear dynamics of high dimensional process data has enabled data-driven RNN-based fault detection algorithms. Previous studies have focused on detecting faults by identifying the discrepancies in data distribution between the faulty and normal data, as reflected in prediction errors generated by RNN models. However, in industrial processes, variations in data distribution can also result from changes in normal control setpoints and compensatory control adjustments in response to disturbances, making it hard to differentiate between normal and faulty conditions. This paper proposes a fault detection method utilizing a long short-term memory (LSTM) encoder–decoder structure with regularized hidden dynamics and reversible instance normalization (RevIN) to compactly represent high-dimensional measurements for effective monitoring. During training, the hidden states of the model are regularized to form a low-dimensional latent space representation of the original multivariate time series data. As a result, the prediction errors of the latent states can be used to monitor the abnormal dynamic variations, while the reconstruction errors of the measured variables are used to monitor the abnormal static variations. Furthermore, the proposed indices can reflect operating conditions, even when the distribution of test data changes, which helps distinguish faults from normal adjustments and disturbances that controllers can settle. Here, data from numerical simulation and the Tennessee Eastman process are used to illustrate the effectiveness of the proposed fault detection method.

42 ENGINEERING↗

DOE OSTI2021

Epistatic Net allows the sparse spectral regularization of deep neural networks for inferring fitness functions

Abstract Despite recent advances in high-throughput combinatorial mutagenesis assays, the number of labeled sequences available to predict molecular functions has remained small for the vastness of the sequence space combined with the ruggedness of many fitness functions. While deep neural networks (DNNs) can capture high-order epistatic interactions among the mutational sites, they tend to overfit to the small number of labeled sequences available for training. Here, we developed Epistatic Net (EN), a method for spectral regularization of DNNs that exploits evidence that epistatic interactions in many fitness functions are sparse. We built a scalable extension of EN, usable for larger sequences, which enables spectral regularization using fast sparse recovery algorithms informed by coding theory. Results on several biological landscapes show that EN consistently improves the prediction accuracy of DNNs and enables them to outperform competing models which assume other priors. EN estimates the higher-order epistatic interactions of DNNs trained on massive sequence spaces-a computational problem that otherwise takes years to solve.

Aghazadeh, Amirali (ORCID:0000000302230873)↗

DOE OSTI2026

Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion

Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here, we introduce a computational framework, regularization by denoising using diffusion models for partial differential equations (RED-DiffEq), by integrating physics-driven inversion and data-driven learning. RED-DiffEq leverages pretrained diffusion models as a regularization mechanism for PDE-governed inverse problems. We apply RED-DiffEq to solve the full waveform inversion problem in geophysics, a challenging seismic imaging technique that seeks to reconstruct high-resolution subsurface velocity models from seismic measurement data. Our method shows enhanced accuracy and robustness compared to benchmark methods. Additionally, it exhibits strong generalization and domain decomposition capacity, enabling the inversion of more complex velocity models with larger domains than those used in training the diffusion model. Our framework can also be directly applied to diverse PDE-governed inverse problems.

Shan, Siming [Yale University, New Haven, CT (Unit↗

DOE OSTI2022

Sequentially regular polymer acceptors featuring flexible spacers for high-performance and mechanically robust all-polymer solar cells

Developing high-performance and mechanically robust polymer solar cells (PSCs) is crucial for realizing wearable power sources. While efficient all-polymer solar cells (all-PSCs) can be fabricated from polymerized small-molecule acceptors (PSMAs) with high optical absorption and electron mobilities, they still show limited mechanical robustness. Here, we achieve highly efficient and mechanically robust all-PSCs by designing a PSMA (PYFS-Reg) containing sequence-regular flexible spacers (FSs). The regular incorporation of the FS units into PSMAs is essential in simultaneously improving the electrical and mechanical properties of blend films. As a result, all-PSCs featuring PYFS-Reg achieve a high power conversion efficiency (PCE = 16.1%) and stretchability (crack onset strain (COS) = 22.4%), outperforming PSMAs without FSs (i.e., PYBDT, PCE = 12.6% and COS = 11.7%) or with randomly distributed FSs (i.e., PYFS-Ran, PCE = 12.2% and COS = 18.1%). Importantly, these all-PSCs are fabricated by an environmentally benign, non-halogenated solvent process. To further demonstrate their feasible applications in wearable devices, we construct intrinsically stretchable (IS) all-PSCs by using PYFS-Reg-based active layers, which exhibit a high PCE (10.6%) and excellent device stretchability (strain at PCE 80% = 36.7%).

14 SOLAR ENERGY↗

DOE OSTI2020

A light weight regularization for wave function parameter gradients in quantum Monte Carlo

The parameter derivative of the expectation value of the energy, ∂E/∂p, is a key ingredient in variational Monte Carlo (VMC) wave function optimization methods. In some cases, a naïve estimate of this derivative suffers from an infinite variance, which inhibits the efficiency of optimization methods that rely on a stable estimate of the derivative. In this work, we derive a simple regularization of the naïve estimator, which is trivial to implement in existing VMC codes, has finite variance, and a negligible bias, which can be extrapolated to zero bias with no extra cost. We use this estimator to construct an unbiased, finite variance estimation of ∂E/∂p for a multi-Slater–Jastrow trial wave function on the LiH molecule and in the optimization of a multi-Slater–Jastrow trial wave function on the CuO molecule. This regularized estimator is a simple and efficient estimator of ∂E/∂p for VMC optimization techniques.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories

Traditional SU⁡(𝑁) lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) 𝑉 𝜆 of the SU⁡(𝑁) gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps {𝜆 ℓ } and monomer tensors on sites labeled by {𝜆 𝑠 }. These tensors naturally define a local site Hilbert space, ℋ$^𝑔_𝑠$, on which gauge transformations act. Gauss’s law introduces an additional index 𝛼 𝑠 =1,2,…,𝒟⁡(ℋ$^𝑔_𝑠$) that labels an orthonormal basis of the gauge-invariant subspace of ℋ$^𝑔_𝑠$. This monomer-dimer tensor-network (MDTN) basis, |{𝜆 𝑠 },{𝜆 ℓ },{𝛼 𝑠 }⟩, of the physical Hilbert space enables the construction of new qubit-regularized SU⁡(𝑁) gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized SU(2) and SU(3) gauge theory in 𝑑 =2 and 𝑑 =3 spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in 𝑑 =1, we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization

We propose a two-dimensional hard-core loop-gas model as a way to regularize the asymptotically free massive continuum quantum field theory that emerges at the Berezinskii-Kosterlitz-Thouless transition. Without fine-tuning, our model can reproduce the universal step-scaling function of the classical lattice X Y model in the massive phase as we approach the phase transition. This is achieved by lowering the fugacity of Fock-vacuum sites in the loop-gas configuration space to zero in the thermodynamic limit. Some of the universal quantities at the Berezinskii-Kosterlitz-Thouless transition show smaller finite size effects in our model as compared to the traditional X Y model. Our model is a prime example of qubit regularization of an asymptotically free massive quantum field theory in Euclidean space-time and helps understand how asymptotic freedom can arise as a relevant perturbation at a decoupled fixed point without fine-tuning. Published by the American Physical Society 2024

Physics↗

DOE OSTI2026

Regularization prescription for the mixing between nonlocal gluon and quark operators

It is well known that in the study of mixing between nonlocal gluon and quark bilinear operators there exists an ambiguity when relating coordinate space and momentum space results. In this work, we show that this ambiguity is due to the lack of a proper regularization prescription of the singularity that arises when the separation between the gluon/quark fields approaches zero. We then demonstrate that dimensional regularization resolves this issue and yields consistent results in both coordinate and momentum space. This prescription is also compatible with lattice extractions of parton distributions from nonlocal operators.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗