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At least 1,333 records · Page 74

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.

Correlated observations↗

TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problems

Deep learning (DL), in particular deep neural networks, by default is purely data-driven and in general does not require physics. This is the strength of DL but also one of its key limitations when applied to science and engineering problems in which underlying physical properties—such as stability, conservation, and positivity—and accuracy are required. DL methods in their original forms are often not capable of respecting the underlying mathematical models or achieving desired accuracy even in big-data regimes. On the other hand, many data-driven science and engineering problems, such as inverse problems, typically have limited experimental or observational data, and DL would overfit the data in this case. Leveraging information encoded in the underlying mathematical models, we argue, not only compensates for missing information in low data regimes but also provides opportunities to equip DL methods with the underlying physics, hence promoting better generalization. This paper develops a model-constrained DL approach and its variant TNet—a Tikhonov neural network—which are capable of learning not only information hidden in the training data but also in the underlying mathematical models to solve inverse problems governed by partial differential equations in low data regimes. We provide the constructions and some theoretical results for the proposed approaches for both linear and nonlinear inverse problems. Since TNet is designed to learn inverse solutions with Tikhonov regularization, it is interpretable: in fact it recovers Tikhonov solutions for linear cases while potentially approximating Tikhonov solutions for nonlinear inverse problems. We also prove that data randomization can enhance not only the smoothness of the networks but also their generalizations. Comprehensive numerical results confirm the theoretical findings and show that with even as little as 1 training data sample for one-dimensional (1D) deconvolution, 5 for an inverse 2D heat conductivity problem, 100 for inverse initial conditions for a time-dependent 2D Burgers’s equation, and 50 for inverse initial conditions for 2D Navier–Stokes equations, TNet solutions can be as accurate as Tikhonov solutions while being several orders of magnitude faster. Furthermore, this is possible owing to the model-constrained term, replications, and randomization.

97 MATHEMATICS AND COMPUTING↗

Constrained Local Approximate Ideal Restriction for Advection-Diffusion Problems

Herein this paper focuses on developing a reduction-based algebraic multigrid (AMG) method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based AMG approach, $\ell \text{AIR}$ (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection-dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion-dominated problems in two or three dimensions. Motivated by the success of $\ell \text{AIR}$ in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion-dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy-minimization AMG methods with the local approximation of ideal operators used in $\ell \text{AIR}$. The resulting constrained $\ell \text{AIR}$ algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that was previously difficult for reduction-based methods.

97 MATHEMATICS AND COMPUTING↗

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗

Library for Evolutionary Algorithms in Python (LEAP)

There are generally three types of scientific software users: users that solve problems using existing science software tools, researchers that explore new approaches by extending existing code, and educators that teach students scientific concepts. Python is a general-purpose programming language that is accessible to beginners, such as students, but also as a language that has a rich scientific programming ecosystem that facilitates writing research software. Additionally, as high-performance computing (HPC) resources become more readily available, software support for parallel processing becomes more relevant to scientific software.There currently are no Python-based evolutionary computation frameworks that support all three types of scientific software users. Moreover, some support synchronous concurrent fitness evaluation that do not efficiently use HPC resources. We pose here a new Python-based EC framework that uses an established generalized unified approach to EA concepts to provide an easy to use toolkit for users wishing to use an EA to solve a problem, for researchers to implement novel approaches, and for providing a low-bar to entry to EA concepts for students. Additionally, this toolkit provides a scalable asynchronous fitness evaluation implementation friendly to HPC that has been vetted on hardware ranging from laptops to the world’s fastest supercomputer, Summit.

Coletti, Mark↗

Neuromorphic Computing is Turing-Complete

Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and GPUs. They have the potential to drive critical use cases such as autonomous vehicles, edge computing and internet of things in the future. For this reason, they are sought to be an indispensable part of the future computing landscape. Neuromorphic systems are mainly used for spike-based machine learning applications, although there are some non-machine learning applications in graph theory, differential equations, and spike-based simulations. These applications suggest that neuromorphic computing might be capable of general-purpose computing. However, general-purpose computability of neuromorphic computing has not been established yet. In this work, we prove that neuromorphic computing is Turing-complete and therefore capable of general-purpose computing. Specifically, we present a model of neuromorphic computing, with just two neuron parameters (threshold and leak), and two synaptic parameters (weight and delay). We devise neuromorphic circuits for computing all the μ-recursive functions (i.e., constant, successor and projection functions) and all the μ-recursive operators (i.e., composition, primitive recursion and minimization operators). Given that the μ-recursive functions and operators are precisely the ones that can be computed using a Turing machine, this work establishes the Turing-completeness of neuromorphic computing.

Date, Prasanna↗

Sampling-based Sublinear Low-rank Matrix Arithmetic Framework for Dequantizing Quantum Machine Learning

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang’s breakthrough quantum-inspired algorithm for recommendation systems [STOC’19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén et al. [STOC’19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all prior results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ℓ 2 -norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

Computer Science↗

Parallel Memory-Independent Communication Bounds for SYRK

In this paper, we focus on the parallel communication cost of multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK). SYRK requires half the computation of general matrix multiplication because of the symmetry of the output matrix. Recent work (Beaumont et al., SPAA '22) has demonstrated that the sequential I/O complexity of SYRK is also a constant factor smaller than that of general matrix multiplication. Inspired by this progress, we establish memory-independent parallel communication lower bounds for SYRK with smaller constants than general matrix multiplication, and we show that these constants are tight by presenting communication-optimal algorithms. The crux of the lower bound proof relies on extending a key geometric inequality to symmetric computations and analytically solving a constrained nonlinear optimization problem. Here, the optimal algorithms use a triangular blocking scheme for parallel distribution of the symmetric output matrix and corresponding computation.

Communication costs↗

Scalable Linked Dynamic Equilibrium (SLiDE)

SLiDE (Scalable Linked Dynamic Equilibrium) replicates the blueNOTE (National Open source Tools for general Equilibrium analysis) datastream from the Wisconsin National Data Consortium. From there, it produces a recursive dynamic computable general equilibrium model of the US states and eventually the global/national economies. The datastream operations have been set up to allow for scalability of both regions and sectors represented. The model has the capability to flexibly define functional forms similar to other general equilibrium model construction software.

Hughes, Caroline↗

BuildingsBench: A Benchmark for Universal Building Load Forecasting [SWR-23-51]

The residential and commercial building stock in the United States is responsible for a significant percentage of energy consumption and greenhouse gas emissions. Electrification of end-uses, as well as decarbonizing the electrical grid through renewable energy sources such as solar and wind, constitutes the pathway to zero-emission buildings. Forecasting day-ahead building energy consumption is an integral part of this solution. Currently, specialized forecasting models are hand-made for each individual building, which is time-consuming, expensive, and leads to duplicated efforts. BuildingsBench is a Python software framework for training and comparing generalized machine learning models for universal building load forecasting. This challenge tasks a single foundational model to generalize its forecasts for a wide variety of buildings, across geographic regions, building types, weather patterns, and more. This software provide code for pre-training such models and subsequently evaluating their performance on a suite of hundreds of diverse real and synthetic buildings. BuildingsBench is a platform for: - Large-scale pretraining with the synthetic Buildings-900K dataset for short-term load forecasting (STLF). Buildings-900K is statistically representative of the entire U.S. building stock and is extracted from the NREL End-Use Load Profiles database. - Benchmarking on two tasks evaluating generalization: zero-shot STLF and transfer learning for STLF. We provide an index-based PyTorch Dataset for large-scale pretraining, easy data loading for multiple real building energy consumption datasets as PyTorch Tensors or Pandas DataFrames, simple (persistence) to advanced (transformer) baselines, metrics management, and more.

Emami, Patrick↗

Spinbox: tools for many-body quantum systems in a Monte Carlo context

Spinbox is a piece of software that facilitates quantum mechanical calculations relevant to Monte Carlo simulation of atomic nuclei. At the front lines of research on the nuclear many-body problem are a large number of supercomputer-scale simulation codes. These codes produce valuable results but can be hard to understand, especially for those without intimate knowledge of the relevant theoretical methods. Thus, tools that fill pedagogical roles are extremely valuable. Spinbox makes it easy for one to replicate and analyze the computational processes relevant to a Quantum Monte Carlo (QMC) simulation that may be difficult to understand/debug/analyze due to the scale of the corresponding simulation software. Spinbox is written in Python using other state-of-the-art Python modules for numerical calculations. While a number of Python libraries exist that are suited to general quantum many-body calculations, the motivation of Spinbox is quite particular. In Diffusion Monte Carlo methods (DMC, GFMC, AFDMC), the central calculation is the imaginary-time propagation of individual samples of the many-body wavefunction. Although quantum wavefunctions generally must be described by a probability distribution over a basis, DMC imbues particles (within one sample) with classical spatial coordinates. This method is unusual, so other Python packages are typically not set up to do this easily. Furthermore, the software has built-in options for nuclear systems assuming isospin symmetry, which can be set up with other libraries but is a nontrivial process to do so. Features: - numerical representation of samples of the many-body wavefunctions, including tensor-product states (used in AFDMC) - numerical representation of many-body operators, including tensor-product operators: general, spin, imaginary-time propagation, etc. - the correct associated arithmetic and algebra, implemented as class methods - classes for representing realistic nuclear two- and three-body Hamiltonians (e.g. Argonne V18, Illinois NNN) - large-scale parallel integration over random variables, crucial for the AFDMC method My goal is to make this package open source so that anyone may use it and contribute to it, particularly other researchers doing AFDMC calculations

Fox, Jordan↗

A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part I: Scheme Description

A novel framework is proposed for the bulk parameterization of rain microphysics: the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS). It is designed to facilitate direct constraint by observations using Bayesian inference. BOSS combines existing process-level microphysical knowledge with flexible process rate formulations and parameters constrained by observations within a Bayesian framework. Furthermore, using a raindrop size distribution (DSD) normalization method that relates DSD moments to one another via generalized power series, generalized multivariate power expressions are derived for the microphysical process rates as functions of a set of prognostic DSD moments. The scheme is flexible and can utilize any number and combination of prognostic moments and any number of terms in the process rate formulations. This means that both uncertainty in parameter values and structural uncertainty associated with the process rate formulations can be investigated systematically, which is not possible using traditional schemes. In this paper, BOSS is compared to two- and three-moment versions of a traditional bulk rain microphysics scheme (denoted as MORR). It is demonstrated that some process formulations in MORR are analytically equivalent to the generalized power expressions in BOSS using one or two terms, while others are not. BOSS is able to replicate the behavior of MORR in idealized one-dimensional rainshaft tests, but with a much more flexible and systematic design. Part II of this study describes the application of BOSS to derive rain microphysical process rates and posterior parameter distributions in Bayesian experiments using Markov chain Monte Carlo sampling constrained by synthetic observations.

58 GEOSCIENCES↗

Vertical Structure and Ice Production Processes of Shallow Convective Postfrontal Clouds over the Southern Ocean in MARCUS. Part I: Observational Study

A study of the vertical structure of postfrontal shallow clouds in the marine boundary layer over the Southern Ocean is presented here. The central question of this two-part study regards cloud phase (liquid/ice) of precipitation, and the associated growth mechanisms. In this first part, data from the Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS) field campaign are analyzed, starting with a 75-h case with continuous sea surface-based thermal instability, modest surface heat fluxes, an open-cellular mesoscale organization, and very few ice nucleating particles (INPs). The clouds are mostly precipitating and shallow (tops mostly around 2 km above sea level), with weak up- and downdrafts, and with cloud-top temperatures generally around –18° to –10°C. Further, the case study is extended to three other periods of postfrontal shallow clouds in MARCUS. While abundant supercooled liquid water is commonly present, an experimental cloud-phase algorithm classifies nearly two-thirds of clouds in the 0° to –5°C layer as containing ice (cloud ice, snow, or mixed phase), implying that much of the precipitation grows through cold-cloud processes. The best predictors of ice presence are cloud-top temperature, cloud depth, and INP concentration. Measures of convective activity and turbulence are found to be poor indicators of ice presence in the studied environment. The water-phase distribution in this cloud regime is explored through numerical simulations in Part II. Significance Statement: Climate models generally predict a lower albedo than observed over the Southern Ocean, and this is largely attributed to a lack of cloudiness, especially in the postfrontal cold sector of midlatitude cyclones. This in turn may be due to an excess of ice in these simulated clouds, resulting in rapid precipitation fallout and an overly brief cloud lifespan. The objective of this study is to examine whether shallow postfrontal clouds over the Southern Ocean are dominated by supercooled drops, or by snow and ice, using data collected by a U.S. Department of Energy Atmospheric Radiation Measurement Mobile Facility deployed aboard an Australian Antarctic supply vessel. We find that these clouds contain much supercooled liquid, even though cloud-top temperatures generally are around –18° to –8°C, and that about two-thirds of the clouds just above the freezing level contain ice. Much of the precipitation appears to grow through cold-cloud processes above the freezing level, rather than drizzle/rain. Updrafts and/or turbulence in convection or in cloud-top generating cells do not initiate much ice, compared to observations elsewhere in a similar temperature range. This may be attributable to the extremely low concentration of ice nucleating particles in this environment. Ultimately, the deepest clouds with the coldest cloud tops are most likely to be ice dominated.

54 ENVIRONMENTAL SCIENCES↗

Assessment of CMIP5 and CMIP6 AMIP Simulated Clouds and Surface Shortwave Radiation Using ARM Observations over Different Climate Regions

The simulations of clouds and surface radiation from 10 CMIP6 models and their CMIP5 predecessors are compared to the ARM ground-based observations over different climate regions. Compared to the ARM radar-lidar derived total cloud fractions (CFT) and cloud fraction vertical distributions over the six selected sites, both CMIP5 and CMIP6 significantly underestimated CFT and low-level CF over the Northern Hemispheric midlatitude sites (SGPC1 and ENAC1), although the biases are generally smaller in CMIP6. Over the tropical oceanic site (TWPC2), 5 out of 10 CMIP6 models better simulated low-level CF than their CMIP5 predecessors. CMIP6 simulations generally agreed well with the ARM observations in CFT and cloud fraction vertical distributions over the tropical continental (MAOM1) and coastal (TWPC3) sites but missed the transitions between dry and wet seasons, similar to CMIP5 simulations. The improvements in downwelling shortwave fluxes (SWdn) at the surface from the majority of CMIP6 compared to CMIP5 primarily resulted from the improved cloud fraction simulations, especially over the SGPC1, ENAC1, and TWPC3 sites. By contrast, both CMIP5 and CMIP6 models exhibited diverse performances of clouds and shortwave radiation over the Arctic site (NSAC1), where CMIP6 models produced more clouds than CMIP5 models, especially for the low-level clouds. The comparisons between observations and CMIP5 and CMIP6 simulations provide valuable quantitative assessments of the accuracy of mean states and variabilities in the model simulations and shed light on general directions to improve climate models in different regions.

54 ENVIRONMENTAL SCIENCES↗

Improving Solution Accuracy and Convergence for Stochastic Physics Parameterizations with Colored Noise

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration methods originally developed for deterministic differential equations are applied naively to stochastic problems. In previous studies, it has been demonstrated that a correction term, known in stochastic analysis as the Itô correction, can help improve solution accuracy for various deterministic numerical schemes and ensure convergence to the physically relevant solution without substantial computational overhead. The usual formulation of the Itô correction is valid only when the stochasticity is represented by white noise. In this study, a generalized formulation of the Itô correction is derived for noises of any color. The formulation is applied to a test problem described by an advection–diffusion equation forced with a spectrum of fast processes. We present numerical results for cases with both constant and spatially varying advection velocities to show that, for the same time step sizes, the introduction of the generalized Itô correction helps to substantially reduce time integration error and significantly improve the convergence rate of the numerical solutions when the forcing term in the governing equation is rough (fast varying); alternatively, for the same target accuracy, the generalized Itô correction allows for the use of significantly longer time steps and, hence, helps to reduce the computational cost of the numerical simulation.

54 ENVIRONMENTAL SCIENCES↗

A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

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. 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. 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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Identifying Genomic Islands with Deep Neural Networks

Background Horizontal gene transfer is the main source of adaptability for bacteria, through which genes are obtained from different sources including bacteria, archaea, viruses, and eukaryotes. This process promotes the rapid spread of genetic information across lineages, typically in the form of clusters of genes referred to as genomic islands (GIs). Different types of GIs exist, and are often classified by the content of their cargo genes or their means of integration and mobility. While various computational methods have been devised to detect different types of GIs, no single method is capable of detecting all types. Results We propose a method, which we call Shutter Island, that uses a deep learning model (Inception V3, widely used in computer vision) to detect genomic islands. The intrinsic value of deep learning methods lies in their ability to generalize. Via a technique called transfer learning, the model is pre-trained on a large generic dataset and then re-trained on images that we generate to represent genomic fragments. We demonstrate that this image-based approach generalizes better than the existing tools. Conclusions We used a deep neural network and an image-based approach to detect the most out of the correct GI predictions made by other tools, in addition to making novel GI predictions. The fact that the deep neural network was re-trained on only a limited number of GI datasets and then successfully generalized indicates that this approach could be applied to other problems in the field where data is still lacking or hard to curate.

Computer Vision↗

Generalizable, fast, and accurate DeepQSPR with fastprop

Abstract Quantitative Structure–Property Relationship studies (QSPR), often referred to interchangeably as QSAR, seek to establish a mapping between molecular structure and an arbitrary target property. Historically this was done on a target-by-target basis with new descriptors being devised to specifically map to a given target. Today software packages exist that calculate thousands of these descriptors, enabling general modeling typically with classical and machine learning methods. Also present today are learned representation methods in which deep learning models generate a target-specific representation during training. The former requires less training data and offers improved speed and interpretability while the latter offers excellent generality, while the intersection of the two remains under-explored. This paper introduces , a software package and general Deep-QSPR framework that combines a cogent set of molecular descriptors with deep learning to achieve state-of-the-art performance on datasets ranging from tens to tens of thousands of molecules. provides both a user-friendly Command Line Interface and highly interoperable set of Python modules for the training and deployment of feedforward neural networks for property prediction. This approach yields improvements in speed and interpretability over existing methods while statistically equaling or exceeding their performance across most of the tested benchmarks. is designed with Research Software Engineering best practices and is free and open source, hosted at github.com/jacksonburns/fastprop.

Burns, Jackson W. (ORCID:0000000206579426)↗