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At least 235 records · Page 13

Current and future directions in network biology

Network biology is an interdisciplinary field bridging computational and biological sciences that has proved pivotal in advancing the understanding of cellular functions and diseases across biological systems and scales. Although the field has been around for two decades, it remains nascent. It has witnessed rapid evolution, accompanied by emerging challenges. These stem from various factors, notably the growing complexity and volume of data together with the increased diversity of data types describing different tiers of biological organization. We discuss prevailing research directions in network biology, focusing on molecular/cellular networks but also on other biological network types such as biomedical knowledge graphs, patient similarity networks, brain networks, and social/contact networks relevant to disease spread. In more detail, we highlight areas of inference and comparison of biological networks, multimodal data integration and heterogeneous networks, higher-order network analysis, machine learning on networks, and network-based personalized medicine. Following the overview of recent breakthroughs across these five areas, we offer a perspective on future directions of network biology. Additionally, we discuss scientific communities, educational initiatives, and the importance of fostering diversity within the field. This article establishes a roadmap for an immediate and long-term vision for network biology.

59 BASIC BIOLOGICAL SCIENCES↗

RivGraph: Automatic extraction and analysis of river and delta channel network topology

River networks sustain life and landscapes by carrying and distributing water, sediment, and nutrients throughout ecosystems and communities. At the largest scale, river networks drain continents through tree-like tributary networks. At typically smaller scales, river deltas and braided rivers form loopy, complex distributary river networks via avulsions and bifurcations.In order to model flows through these networks or analyze network structure, the topology, or connectivity, of the network must be resolved. Additionally, morphologic properties of each river channel as well as the direction of flow through the channel inform how fluxes travel through the network’s channels. Riv Graphis a Python package that automates the extraction and characterization of river channel networks from a user-provided binary image, or mask, of a channel network (Fig. 1). Masks may be derived from (typically remotely-sensed) imagery, simulations, or even hand-drawn. RivGraph will create explicit representations of the channel network by resolving river centerlines as links, and junctions as nodes. Flow directions are solved for each link of the network without using auxiliary data, e.g., a digital elevation model (DEM). Morphologic properties are computed as well, including link lengths, widths, sinuosities, branching angles,and braiding indices. If provided,RivGraph will preserve georeferencing information of the mask and will export results as ESRI shapefiles, GeoJSONs, and GeoTIFFs for easy import into GIS software.RivGraph can also return extracted networks as networkx objects for convenient interfacing with the full-featured networkx package (Hagberg et al., 2008). Finally, RivGraph offers a suite of topologic metrics that were specifically designed for river channel network analysis (Tejedor et al., 2015b).

54 ENVIRONMENTAL SCIENCES↗

An Evaluation of the Effect of Network Cost Optimization for Leadership Class Supercomputers

Dragonfly-based networks are an extensively deployed network topology in large-scale high-performance computing due to their cost-effectiveness and efficiency. The US will soon have three Exascale supercomputers for leadership class workloads deployed using dragonfly networks. Compared to indirect networks of similar scale, the dragonfly network has considerably reduced cable lengths, cable counts, and switch counts, resulting in significant network cost savings for a given system size, however, these cost reductions result in reduced global minimal paths and more challenging routing. Additionally, large scale dragonfly networks often require a taper at the global link level, resulting in less bisection bandwidth than is achievable in other traditional non-blocking topologies of equivalent scale. While dragonfly networks have been extensively studied, they have yet to be fully evaluated in an extreme scale (i.e., exascale) system that targets capability workloads. In this paper, we present the results of the first large scale evaluation of a dragonfly network on an exascale system (Frontier) and compare its behavior to a similar scale fat-tree network on a previous generation TOP500 system (Summit). This evaluation aims to determine the effect of network cost optimizations by measuring a tapered topology’s impact on capability workloads. Our evaluation is based on a collection of synthetic microbenchmarks, mini-apps, and full scale applications. It compares the scaling efficiencies of each benchmark between the dragonfly-based Frontier and the fat-tree-based Summit systems. Our results show that a dragonfly network is $\sim \mathbf{3 0 \%}$ more cost efficient than a fat-tree topology, which amortizes to $\sim 3 \%$ of an exascale system cost. Furthermore, while tapered dragonfly networks impose significant tradeoffs, the impacts are not as broad as initially thought and are mostly seen in applications with global communication patterns, particularly all-to-all (e.g., FFT-based algorithms), but also local communication patterns (e.g., nearest-neighbor algorithms) that are sensitive to network performance variability.

Khan, Awais↗

MCS+: An Efficient Algorithm for Crawling the Community Structure in Multiplex Networks

In this article, we consider the problem of crawling a multiplex network to identify the community structure of a layer-of-interest. A multiplex network is one where there are multiple types of relationships between the nodes. In many multiplex networks, some layers might be easier to explore (in terms of time, money etc.). We propose MCS+, an algorithm that can use the information from the easier to explore layers to help in the exploration of a layer-of-interest that is expensive to explore. We consider the goal of exploration to be generating a sample that is representative of the communities in the complete layer-of-interest. This work has practical applications in areas such as exploration of dark (e.g., criminal) networks, online social networks, biological networks, and so on. For example, in a terrorist network, relationships such as phone records, e-mail records, and so on are easier to collect; in contrast, data on the face-to-face communications are much harder to collect, but also potentially more valuable. We perform extensive experimental evaluations on real-world networks, and we observe that MCS+ consistently outperforms the best baseline—the similarity of the sample that MCS+ generates to the real network is up to three times that of the best baseline in some networks. We also perform theoretical and experimental evaluations on the scalability of MCS+ to network properties, and find that it scales well with the budget, number of layers in the multiplex network, and the average degree in the original network.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

A Scalable Quantum Cryptography Network for Protected Automation Communication (Final Report)

This is the final report for a CEDS-funded project aimed at developing a new quantum technology for securing utility communication networks used to control and monitor electrical grid equipment. Securing these control networks represents a unique challenge as the performance of the security solution has a direct impact on the stability and reliability of the electrical grid. Traditional, software-based solutions - developed for information networks - are not suitable for utility control networks because they introduce latency, require burdensome maintenance and upgrades, are often incompatible with legacy equipment, and introduce operational complexity that reduces grid reliability. Consequently, many U.S. utilities do not use existing solutions and, instead, protect their critical control networks through the careful isolation and obscuration of their networked equipment. With more utilities embracing grid automation, the attack surface that utilities must defend from hackers has grown to an unmanageable size. To address this situation, Qubitekk and its partners proposed and developed a hardware-based solution that can secure critical control networks without negatively impacting grid performance. This new solution is based on quantum key distribution (QKD) techniques that guarantee secure key generation and distribution across a utility control network. Through deployment and field testing of a prototype QKD system, we have shown that this solution delivers long-term network security, is technically feasible to implement and maintain on a utility’s distribution substation network and does not negatively impact grid operations. In addition, the project has identified and solved key challenges associated with generating, transmitting, and measuring coherent photonic quantum states on a real-world fiber optic network. These additional findings are playing a critical role in advancing quantum networks for quantum computing applications. An overview of the QKD prototype development effort, field testing activities and results, and additional findings relevant to emerging quantum networks are presented in this report.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Enhancing Security and Resiliency in Operational Technology Environments Through Network Slicing and Federated Learning

The growing convergence of Information Technology (IT) and Operational Technology (OT) within Industry 4.0 environments has introduced new demands on industrial network infrastructure. As cyber-physical systems become increasingly interconnected, ensuring the secure, timely, and efficient exchange of critical data is essential. This thesis explores how network slicing, a method of creating isolated virtual network segments, can be applied within OT environments to address challenges such as latency, security, and resource allocation. The first research question addressed in this thesis is: How can OT networks take advantage of NFV and SDN technology to become cyber resilient? This study examines the operational, security, and architectural implications of introducing network slicing into traditionally static OT infrastructures such as Industrial Control Systems (ICS) and SCADA. Through simulated deployments and case studies, the research demonstrates how slicing enables better isolation between critical and non-critical services, thereby improving response time, throughput, and security in sensitive environments. The second question considers: How to dynamically implement network slicing and take advantage of network resources towards integrating decentralized machine learning? In response, this thesis proposes a framework that combines Software-Defined Networking (SDN), Network Function Virtualization (NFV), and Federated Learning (FL) to enable real-time analytics while maintaining data locality. The proposed approach reduces the burden on centralized infrastructure and minimizes privacy risks by supporting on-site training of models across distributed OT nodes, coordinated through dynamically allocated network slices. The third focus explores: How slicing helps to increase the resiliency of OT networks through the orchestration of a dynamic DMZ? To answer this, the thesis presents a method for creating and managing Dynamic Demilitarized Zones (DMZs) using network slicing. This enables flexible and automated isolation of sensitive subsystems during threat scenarios or high-risk operations. Coupled with intelligent orchestration and containerized security services, the dynamic DMZ significantly enhances the system's ability to respond to cyber incidents without halting production. Ultimately, this thesis contributes a comprehensive architecture that blends network slicing with machine learning, secure segmentation, and automation, paving the way for resilient, adaptive, and intelligent OT environments. Performance evaluations across multiple scenarios show improvements in system reliability, threat response time, model accuracy, and resource utilization, providing a strong foundation for future industrial automation systems.

Rodiles Delgado, Brian G↗

Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness

We report the accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory answers to the problems of approximation and optimization, much less is known about the theory of generalization. Most existing theoretical works for generalization fail to explain the performance of neural networks in practice. To derive a meaningful bound, we study the generalization error of neural networks for classification problems in terms of data distribution and neural network smoothness. We introduce the cover complexity (CC) to measure the difficulty of learning a data set and the inverse of the modulus of continuity to quantify neural network smoothness. A quantitative bound for expected accuracy/error is derived by considering both the CC and neural network smoothness. Although most of the analysis is general and not specific to neural networks, we validate our theoretical assumptions and results numerically for neural networks by several data sets of images. The numerical results confirm that the expected error of trained networks scaled with the square root of the number of classes has a linear relationship with respect to the CC. We also observe a clear consistency between test loss and neural network smoothness during the training process. In addition, we demonstrate empirically that the neural network smoothness decreases when the network size increases whereas the smoothness is insensitive to training dataset size.

97 MATHEMATICS AND COMPUTING↗

Updated Application of Frequency of Detection Methods for the INL Site Ambient Air Monitoring Network

This report presents a quantitative assessment of the current INL Site air monitoring network using frequency of detection (FD) methods. The first assessment of the INL network was performed in 2015 and made recommendations for improving the network. As a result of changes made in response to the recommendations and the addition of new source locations, the network was modified and reassessed in 2017. Since 2017, administration of the air sampling program has been consolidated under one contractor, which resulted in additional changes to the network (sampler numbers and locations) and changes in radionuclide detection levels. As a result of these changes and others, an updated assessment of the INL Site ambient air monitoring network was performed. The same two exposure scenarios used in previous assessments were used for this assessment: a resident scenario and a shepherd/rancher scenario. The resident was assumed to be continuously present at their residence/business/farm operation outside the INL Site boundary while the shepherd/rancher was assumed to be present 24-hours at the nearest INL grazing allotment boundary in each of the 22.5-degree sectors along the sector centerline from each source. Updates to both the resident and shepherd/rancher receptor locations were included. Other changes include updates to flow rates for stack sources, expansion of the list of important radionuclides based on the most recent National Emission Standards for Hazardous Pollutants (NESHAPs) analysis, and updated dose coefficients. The assessment was conducted to determine whether the current INL monitoring network is capable of detecting releases of important radionuclides from INL Site sources that have the potential to exceed a conservative dose threshold for the two exposure scenarios. The assessment revealed that for the resident scenario, the current network meets the desired performance objective (FD = 95%) for all radionuclides and sources except for Cl-36 from the TRA-770 stack (94.4%). For the shepherd/rancher scenario, the FD performance objective is met for all radionuclides and sources except tritium from MFC-774 and TAN 679 (91% for both). An investigation of reported emissions for the past three years revealed that Cl 36 is not emitted from TRA-770, and routine tritium emissions from MFC-774 and TAN-679 are very small and the sources are likely incapable of emitting enough tritium to cause a release that should be detectable by the monitoring network. This assessment is based on a conservative dose threshold. This coupled with fact that the FD for Cl 36 is only slightly less than the performance objective and Cl-36 is not emitted from TRA-770, modifying the network (i.e. adding another sampler, increasing sampler flow rate, moving samplers) to meet the 95% performance objective for this radionuclide/source/receptor scenario is not warranted. Similarly, because tritium emissions from MFC-774 and TAN-679 are very small and these two sources are likely incapable of causing a dose due to tritium release that should be detectable by the network, modifications to increase tritium detection for these sources is also unwarranted at this time. However, if it is required to meet the performance objective for tritium for all sources and receptor scenarios, additional analysis determined the FD could be raised from 91% to > 99% for both sources by adding two tritium samplers to the network.

61 RADIATION PROTECTION AND DOSIMETRY↗

Fast GPU-Based Generation of Large Graph Networks From Degree Distributions

Synthetically generated, large graph networks serve as useful proxies to real-world networks for many graph-based applications. The ability to generate such networks helps overcome several limitations of real-world networks regarding their number, availability, and access. Here, we present the design, implementation, and performance study of a novel network generator that can produce very large graph networks conforming to any desired degree distribution. The generator is designed and implemented for efficient execution on modern graphics processing units (GPUs). Given an array of desired vertex degrees and number of vertices for each desired degree, our algorithm generates the edges of a random graph that satisfies the input degree distribution. Multiple runtime variants are implemented and tested: 1) a uniform static work assignment using a fixed thread launch scheme, 2) a load-balanced static work assignment also with fixed thread launch but with cost-aware task-to-thread mapping, and 3) a dynamic scheme with multiple GPU kernels asynchronously launched from the CPU. The generation is tested on a range of popular networks such as Twitter and Facebook, representing different scales and skews in degree distributions. Results show that, using our algorithm on a single modern GPU (NVIDIA Volta V100), it is possible to generate large-scale graph networks at rates exceeding 50 billion edges per second for a 69 billion-edge network. GPU profiling confirms high utilization and low branching divergence of our implementation from small to large network sizes. For networks with scattered distributions, we provide a coarsening method that further increases the GPU-based generation speed by up to a factor of 4 on tested input networks with over 45 billion edges.

97 MATHEMATICS AND COMPUTING↗

Determining flow directions in river channel networks using planform morphology and topology

Abstract. The abundance of global, remotely sensed surface water observations has accelerated efforts toward characterizing and modeling how water moves across the Earth's surface through complex channel networks. In particular, deltas and braided river channel networks may contain thousands of links that route water, sediment, and nutrients across landscapes. In order to model flows through channel networks and characterize network structure, the direction of flow for each link within the network must be known. In this work, we propose a rapid, automatic, and objective method to identify flow directions for all links of a channel network using only remotely sensed imagery and knowledge of the network's inlet and outlet locations. We designed a suite of direction-predicting algorithms (DPAs), each of which exploits a particular morphologic characteristic of the channel network to provide a prediction of a link's flow direction. DPAs were chained together to create “recipes”, or algorithms that set all the flow directions of a channel network. Separate recipes were built for deltas and braided rivers and applied to seven delta and two braided river channel networks. Across all nine channel networks, the recipe-predicted flow directions agreed with expert judgement for 97 % of all tested links, and most disagreements were attributed to unusual channel network topologies that can easily be accounted for by pre-seeding critical links with known flow directions. Our results highlight the (non)universality of process–form relationships across deltas and braided rivers.

54 ENVIRONMENTAL SCIENCES↗

Evaluating software defined networking solutions to reduce the digital attack surface of nuclear security systems

Most nuclear security systems used today were not designed for today’s threat environment. Systems that were intended to be stand alone are now interconnected. Devices that have a single purpose are built on multi-purpose platforms and communication protocols that, while effective, have no ability to authenticate authorized versus unauthorized commands. These attributes provide an attacker significant ability to affect the system, pivot throughout the interconnected networks, and remain undetected if he/she is able to compromise a single node. Software defined networking (SDN) has been used for years by information technology (IT) cloud service providers to quickly provision or remove servers or other systems to meet changing demand. The same concept has recently been applied to operational technology (OT) systems to enable very fast failover on critical systems that have stringent and deterministic (<5ms) transmit/receive times. By carefully engineering the communication flows through a network using preplanned routes and specific pathways it is possible to achieve deterministic and extremely reliable message delivery even when components fail. This engineering approach to network design has added security benefits including securing the networking control plane, eliminating network scanning and mapping, inhibiting ARP spoofing and host masquerading, eliminating unauthorized network pivoting and enabling greater situational awareness on the network. SDN in OT environments is new but early testing in electrical power and other critical infrastructure has shown it to be a very powerful tool for building reliable networks and reducing the digital attack surface of the network. The authors tested a software defined network switch on a simple physical protection system with components commonly found in nuclear security systems and found improved mitigations to denial of service attacks, lateral movement and network reconnaissance. The paper details the tests and their results.

Cyber security, Nuclear security, software defined↗

Stochasticity and robustness in spiking neural networks

Despite drawing inspiration from biological systems which are inherently noisy and variable, artificial neural networks have been shown to require precise weights to carry out the task which they are trained to accomplish. This creates a challenge when adapting these artificial networks to specialized execution platforms which may encode weights in a manner which restricts their accuracy and/or precision.Reflecting back on the non-idealities which are observed in biological systems, we investigated the effect these properties have on the robustness of spiking neural networks under perturbations to weights. First, we examined techniques extant in conventional neural networks which resemble noisy processes, and postulated they may produce similar beneficial effects in spiking neural networks. Second, we evolved a set of spiking neural networks utilizing biological non-idealities to solve a pole-balancing task, and estimated their robustness. We showed it is higher in networks using noisy neurons, and demonstrated that one of these networks can perform well under the variance expected when a hafnium-oxide based resistive memory is used to encode synaptic weights. Lastly, we trained a series of networks using a surrogate gradient method on the MNIST classification task. We confirmed that these networks demonstrate similar trends in robustness to the evolved networks. We discuss these results and argue that they display empirical evidence supporting the role of noise as a regularizer which can increase network robustness.

97 MATHEMATICS AND COMPUTING↗

Xylem network connectivity and embolism spread in grapevine( Vitis vinifera L.)

Abstract Xylem networks are vulnerable to the formation and spread of gas embolisms that reduce water transport. Embolisms spread through interconduit pits, but the three-dimensional (3D) complexity and scale of xylem networks means that the functional implications of intervessel connections are not well understood. Here, xylem networks of grapevine (Vitis vinifera L.) were reconstructed from 3D high-resolution X-ray micro-computed tomography (microCT) images. Xylem network performance was then modeled to simulate loss of hydraulic conductivity under increasingly negative xylem sap pressure simulating drought stress conditions. We also considered the sensitivity of xylem network performance to changes in key network parameters. We found that the mean pit area per intervessel connection was constant across 10 networks from three, 1.5-m stem segments, but short (0.5 cm) segments fail to capture complete network connectivity. Simulations showed that network organization imparted additional resistance to embolism spread beyond the air-seeding threshold of pit membranes. Xylem network vulnerability to embolism spread was most sensitive to variation in the number and location of vessels that were initially embolized and pit membrane vulnerability. Our results show that xylem network organization can increase stem resistance to embolism spread by 40% (0.66 MPa) and challenge the notion that a single embolism can spread rapidly throughout an entire xylem network.

Wason, Jay↗

Throughput Measurements and Profile Analysis of Cloud Networks

Cloud networks utilize virtual connections to connect virtual machines distributed across cloud sites. They are increasingly deployed due to flexible provisioning using software and cost-effectiveness in not requiring to build physical network infrastructure. However, their extensive virtualization makes it unclear how well the established practices of conventional networks translate to them. Here, we study throughput measurements over a Google Cloud network using a matching hardware emulated conventional network, which provide production and exploratory conditions, respectively. The measurements span connections representing local, cross-continental and around the Earth distances. We study the effects of parallel flows, congestion control algorithms and retransmissions on the network throughput profile expressed as a function of RTT. We compare the throughput profile of Google Cloud network with those of emulated network under various loss conditions, including those too disruptive or expensive in the former. Our analysis based on the concave-convex shape and utilization-concavity coefficients of throughput profiles indicates an overall agreement of performance between the two networks, thereby justifying the use of conventional network emulations to analyze cloud networks. In terms of practical use, our study establishes that BBR and BBRv2 alpha TCP achieve higher throughput compared to loss-based congestion control algorithms under most network configurations, especially, under losses at large RTT.

Phanekham, Derek [Southern Methodist Univ., Dallas↗

Path-synchronous performance monitoring of interconnection networks based on source code attribution

Examples disclosed herein relate to path-synchronous performance monitoring of an interconnection network based on source code attribution. A processing node in the interconnection network has a profiler module to select a network transaction to be monitored, determine a source code attribution associated with the network transaction to be monitored, and issue a network command to execute the network transaction to be monitored. A logger module creates, in a buffer, a node temporal log associated with the network transaction and the network command. A drainer module periodically captures the node temporal log. The processing node has a network interface controller to receive the network command and mark a packet generated for the network command to be temporally tracked and attributed back to the source code attribution at each hop of the interconnection network traversed by the marked packet.

Chabbi, Milind M.↗

Identifying strengths and weaknesses of methods for computational network inference from single-cell RNA-seq data

Single-cell RNA-sequencing (scRNA-seq) offers unparalleled insight into the transcriptional programs of different cellular states by measuring the transcriptome of thousands of individual cells. An emerging problem in the analysis of scRNA-seq is the inference of transcriptional gene regulatory networks and a number of methods with different learning frameworks have been developed to address this problem. Here, we present an expanded benchmarking study of eleven recent network inference methods on seven published scRNA-seq datasets in human, mouse, and yeast considering different types of gold standard networks and evaluation metrics. We evaluate methods based on their computing requirements as well as on their ability to recover the network structure. We find that, while most methods have a modest recovery of experimentally derived interactions based on global metrics such as Area Under the Precision Recall curve, methods are able to capture targets of regulators that are relevant to the system under study. Among the top performing methods that use only expression were SCENIC, PIDC, MERLIN or Correlation. Addition of prior biological knowledge and the estimation of transcription factor activities resulted in the best overall performance with the Inferelator and MERLIN methods that use prior knowledge outperforming methods that use expression alone. We found that imputation for network inference did not improve network inference accuracy and could be detrimental. Comparisons of inferred networks for comparable bulk conditions showed that the networks inferred from scRNA-seq datasets are often better or at par with the networks inferred from bulk datasets. Our analysis should be beneficial in selecting methods for network inference. At the same time, this highlights the need for improved methods and better gold standards for regulatory network inference from scRNAseq datasets.

59 BASIC BIOLOGICAL SCIENCES↗

SD-WAN Evaluation Criteria for a Defense Information Systems Network Expeditionary Customer Edge

The Defense Information Systems Agency (DISA) has identified a service provision gap midway between the capacity and capability of a Defense Information Systems Network (DISN) transport Edge Points of Presence (POP) and U.S. Department of Defense (DoD) Enterprise Classified Travel Kit (DECTK). Some deployed force 100-user Tactical Operations Centers are in field locations far removed from the DISN transport core, in challenging environmental conditions with limitations on space, weight, power, and cooling for network equipment. As part of a multi-phase project, Pacific Northwest National Laboratory (PNNL) will gather and analyze requirements, design, develop, prototype, and test a miniaturized and ruggedized DISN Customer Edge POP scaled to support approximately 100 users in a field Tactical Operations Center. An Expeditionary Customer Edge (ECE) will be more suitable for field deployment than a DISN transport Edge POP, using ruggedized hardware and network function virtualization (NFV) to operate in challenging field environmental conditions, plus reduce weight, power, and cooling requirements. A key enabling technology for ECE is Software Defined Wide Area Networking (SD-WAN). This document provides: • A brief overview of SD-WAN use cases and how they apply to ECE • How SD-WAN technology compares to existing networks like DISN that use Optical Transport Networking (OTN) and Multiprotocol Label Switching (MPLS) • SD-WAN functional requirements relevant to ECE • A description of an ECE Virtual Prototype, including simulated wide area network paths and a DISN-representative implementation of MPLS, in Cisco Modeling Labs • Detailed network flow walkthroughs • Evaluation criteria based on ECE-relevant SD-WAN functional requirements Finally, an appendix provides an informal evaluation of Speedify—a commercial retail Virtual Private Network service—against the ECE SD-WAN evaluation criteria.

42 ENGINEERING↗

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗