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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Multiverse: Bayesian model selection for neural networks

Multiverse is a code repository for a set of tools for Bayesian model selection for neural networks. The goal of the tools is to provide capabilities for selecting among prior and model specifications for Bayesian neural networks. Multiverse will include tools for creating Bayesian neural networks, evaluating the Bayesian model evidence, and performing inference in Bayesian neural networks. These components are written in Python, a high-level programming language that takes advantage of the Python ecosystem of high-quality open-source packages for machine learning and signal processing.

Klein, Natalie↗
DOE OSTI2025

AutoFocus: AI/ML-driven real-time wavefront diagnostics to autonomously align and optimize X-ray optics

We present an integrated system that combines advanced wavefront diagnostics with artificial intelligence (AI) to automate and optimize X-ray optics at synchrotron beamlines. This system couples real-time wavefront sensing with AI-driven control algorithms to achieve precise beam alignment, stabilization, and performance optimization. A key feature is the use of multi-fidelity transfer learning, which enables knowledge gained from both real-world beamline optimizations and ultra-realistic digital twin simulations to be effectively applied to in situ optimization. By leveraging multi-objective bayesian optimization, the system continuously refines its performance, reducing optimization time and minimizing the need for manual adjustments. Designed for seamless deployment, it operates with existing beamline hardware and provides an intuitive graphical interface. Initial deployments at the advanced photon source beamlines have demonstrated its ability to enhance beam stability, improve reproducibility, and significantly streamline alignment procedures. This AI-enhanced control framework represents a significant step toward fully autonomous beamline operation in next-generation synchrotron facilities.

Rebuffi, Luca [Argonne National Laboratory (ANL), ↗
DOE OSTI2021

A Data-Fusion Method using Bayesian Approach to Enhance Raw Data Accuracy of Position and Distance Measurements for Connected Vehicles

Accurate positioning of vehicles is a critical element of autonomous and connected vehicle systems. Most of other studies heavily focused on enhancing simultaneous localization and mapping (SLAM) methods, i.e., constructing or updating a map of an unknown environment and tracking an object within the map. This paper provides a method that can, in addition to existing SLAM or relevant methods, enhance the raw measurements of position and distance. The basic idea of this study is to identify and update the error distribution of each data source by combining all available information. A Bayesian approach was incorporated to estimate and update the error distribution of individual data sources or sensors. The proposed method can be conducted in real-time environments, and a self-learning scheme determines whether enough data has been collected to further improve the accuracy of such measurements. The simulated experiments show that the proposed model noticeably improves the accuracy of position and distance measurements. Especially, the estimated biases of position coordinates and distance measures are very close to the biases of true error distributions, with the R-squared over 0.98. A similar approach can also be utilized to enhance accuracy of other sensors or measurements in connected vehicle or relevant systems, where multi-data sources are available.

Lim, Hyeonsup↗
DOE OSTI2016

Imputing data that are missing at high rates using a boosting algorithm

Traditional multiple imputation approaches may perform poorly for datasets with high rates of missingness unless many m imputations are used. This paper implements an alternative machine learning-based approach to imputing data that are missing at high rates. Here, we use boosting to create a strong learner from a weak learner fitted to a dataset missing many observations. This approach may be applied to a variety of types of learners (models). The approach is demonstrated by application to a spatiotemporal dataset for predicting dengue outbreaks in India from meteorological covariates. A Bayesian spatiotemporal CAR model is boosted to produce imputations, and the overall RMSE from a k-fold cross-validation is used to assess imputation accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning

Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this work, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by 1.26x,1.29x,1.47x, and 2.65 x, respectively.

42 ENGINEERING↗
DOE OSTI2016

Semiparametric modeling: Correcting low-dimensional model error in parametric models

In this paper, a semiparametric modeling approach is introduced as a paradigm for addressing model error arising from unresolved physical phenomena. Our approach compensates for model error by learning an auxiliary dynamical model for the unknown parameters. Practically, the proposed approach consists of the following steps. Given a physics-based model and a noisy data set of historical observations, a Bayesian filtering algorithm is used to extract a time-series of the parameter values. Subsequently, the diffusion forecast algorithm is applied to the retrieved time-series in order to construct the auxiliary model for the time evolving parameters. The semiparametric forecasting algorithm consists of integrating the existing physics-based model with an ensemble of parameters sampled from the probability density function of the diffusion forecast. To specify initial conditions for the diffusion forecast, a Bayesian semiparametric filtering method that extends the Kalman-based filtering framework is introduced. In difficult test examples, which introduce chaotically and stochastically evolving hidden parameters into the Lorenz-96 model, we show that our approach can effectively compensate for model error, with forecasting skill comparable to that of the perfect model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Voltron Compatible Whole Building Root-Fault Detection and Diagnosis

Buildings consume more than 40% of primary energy in the U.S. Malfunctioning sensors, components, and control systems, as well as degrading components in Heating, Ventilating and Air-conditioning (HVAC) and lighting systems are main reasons for energy waste and unsatisfactory indoor environment. Field studies have shown that an energy saving of 5-30% of total building energy consumption and improved indoor air quality can be achieved by simply applying automated fault detection and diagnosis (AFDD), followed by corrections even if these are not done in real time. Extensive research has been made on the development of component level AFDD tools in the past two decades. However, in recent years, the development of method for a whole building level AFDD has received much attention. Here, a whole building fault refers to a fault happening in one subsystem but impact on more than one subsystems, or has a significant impact on building performances, such as building’s energy consumption. Existing component level AFDD tools could fail to detect or give false alarm for faults that trigger abnormalities in multiple subsystems. Isolating such whole building faults, which have impacts on multiple subsystems, is also challenging by simply using component based AFDD solutions. On the other hand, it might be more cost-effective for medium- or small-sized commercial buildings that have subsystems (e.g. primary cooling subsystem, air loop subsystem, heating subsystem, lighting subsystem, etc.) to install one whole building level AFDD tool, rather than many component level AFDD tools, to focus on significant faults. The focus of this project is firstly to provide training opportunities in building AFDD research area for undergraduate students and to develop a workforce pipeline in building sciences. The objective of the proposed research activities is to develop cost-effective and scalable AFDD solutions for whole building level faults. The developed AFDD solution is VOLTTRONTM compatible to further increase its plug-n-play capacity and the market penetration. VOLTTRONTM is an open-source innovative distributed control and sensing software platform developed by the Pacific Northwest National Laboratory. A VOLTTRONTM compatible AFDD tool brings the benefits such as low-cost deployment, and better building to grid integration, etc. The performance of the developed whole building AFDD tools is evaluated using data collected from a mixed-use medium-sized university campus building. Another significant goal of this project is to engage undergraduate students in research activities and expose them to building control and AFDD fields. A demonstration building – Nesbitt Hall at Drexel University is identified for this study. This demonstration building has a typical HVAC system configuration, which includes a water-cooled chiller system, three variable air volume (VAV) air handling unit (AHU) systems, and a hydronic heating system. Faults, that are expected to have a whole building level impact, are artificially implemented in this demonstration building for three different seasons. Building data have been collected in this project, which include fault free building automation system (BAS) data and BAS data that contain system behaviors caused by artificially implemented and naturally occurred faults. These collected data are used to evaluate the developed whole building AFDD tools. A data-driven method, which includes a weather and schedule-based pattern matching (WPM) method and Feature based Principal Component Analysis (FPCA) method, is developed for whole building level fault detection. Parameter sensitivity tests, including snapshot window size, data sample searching pool size, etc., are implemented to evaluate the impacts of various WPM-FPCA parameters. A data-driven and expert knowledge/rule-based method using Bayesian Network (BN) and WPM is developed for whole building level fault diagnosis. The developed WPM-BN method, which includes a two-layer BN structure model and BN parameters, are either learned from baseline data or developed from expert knowledge. The developed whole building AFDD tools are evaluated using BAS data collected from the demonstration building. Using the evaluation data set, the WPM-FPCA fault detection method is evaluated under two different Principle Component (PC) retention rates, i.e., 0.65 retention rate and 0.95 retention rate. It is observed that when using 0.65 PC retention rate, the WPM-FPCA fault detection method achieves a 79% fault detection rate (this rate reaches to 85% when including the six make-up fault test cases discussed in the next bullet), while when using 0.95 PC retention rate, the WPM-FPCA fault detection method achieves 100% fault detection rate (this rate remains to be 100% when including the six make-up fault test cases). Under both PC retention rates, the WPM-FPCA fault detection method demonstrates 0% false alarm rates. Using the evaluation data set, the developed WPM-BN fault diagnosis method has successfully diagnosed thirteen (13) faults out of the fourteen (14) fault test cases. The one mis-diagnosed case exhibits fewer fault symptoms in different subsystems, when compared with other fault test cases. Overall speaking, the developed whole building AFDD solutions demonstrate satisfactory fault detection/diagnosis accuracy with very low false alarm rate. Lastly, a survey and market study has been performed to understand the existing AFDD market, including its gaps and needs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Automating Sensor Characterization with Bayesian Optimization

The development of novel instrumentation requires an iterative cycle with three stages: design, prototyping, and testing. Recent advancements in simulation and nanofabrication techniques have significantly accelerated the design and prototyping phases. Nonetheless, detector characterization continues to be a major bottleneck in device development. During the testing phase, a significant time investment is required to characterize the device in different operating conditions and find optimal operating parameters. The total effort spent on characterization and parameter optimization can occupy a year or more of an expert's time. In this work, we present a novel technique for automated sensor calibration that aims to accelerate the testing stage of the development cycle. This technique leverages closed-loop Bayesian optimization (BO), using real-time measurements to guide parameter selection and identify optimal operating states. We demonstrate the method with a novel low-noise CCD, showing that the machine learning-driven tool can efficiently characterize and optimize operation of the sensor in a couple of days without supervision of a device expert.

Cuevas-Zepeda, Julian [Chicago U., KICP; Chicago U↗
DOE OSTI2021

Latent map Gaussian processes for mixed variable metamodeling

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. Here we introduce latent map Gaussian processes (LMGPs) that inherit the attractive properties of GPs and are also applicable to mixed data which have both quantitative and qualitative inputs. The core idea behind LMGPs is to learn a continuous, low-dimensional latent space or manifold which encodes all qualitative inputs. To learn this manifold, we first assign a unique prior vector representation to each combination of qualitative inputs. We then use a low-rank linear map to project these priors on a manifold that characterizes the posterior representations. As the posteriors are quantitative, they can be directly used in any standard correlation function such as the Gaussian or Matern. Hence, the optimal map and the corresponding manifold, along with other hyperparameters of the correlation function, can be systematically learned via maximum likelihood estimation. Through a wide range of analytic and real-world examples, we demonstrate the advantages of LMGPs over state-of-the-art methods in terms of accuracy and versatility. In particular, we show that LMGPs can handle variable-length inputs, have an explainable neural network interpretation, and provide insights into how qualitative inputs affect the response or interact with each other. We also employ LMGPs in Bayesian optimization and illustrate that they can discover optimal compound compositions more efficiently than conventional methods that convert compositions to qualitative variables via manual featurization.

42 ENGINEERING↗
DOE OSTI2024

Stochastic machine learning via sigma profiles to build a digital chemical space

This work establishes a different paradigm on digital molecular spaces and their efficient navigation by exploiting sigma profiles. To do so, the remarkable capability of Gaussian processes (GPs), a type of stochastic machine learning model, to correlate and predict physicochemical properties from sigma profiles is demonstrated, outperforming state-of-the-art neural networks previously published. The amount of chemical information encoded in sigma profiles eases the learning burden of machine learning models, permitting the training of GPs on small datasets which, due to their negligible computational cost and ease of implementation, are ideal models to be combined with optimization tools such as gradient search or Bayesian optimization (BO). Gradient search is used to efficiently navigate the sigma profile digital space, quickly converging to local extrema of target physicochemical properties. While this requires the availability of pretrained GP models on existing datasets, such limitations are eliminated with the implementation of BO, which can find global extrema with a limited number of iterations. A remarkable example of this is that of BO toward boiling temperature optimization. Holding no knowledge of chemistry except for the sigma profile and boiling temperature of carbon monoxide (the worst possible initial guess), BO finds the global maximum of the available boiling temperature dataset (over 1,000 molecules encompassing more than 40 families of organic and inorganic compounds) in just 15 iterations (i.e., 15 property measurements), cementing sigma profiles as a powerful digital chemical space for molecular optimization and discovery, particularly when little to no experimental data is initially available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

BAYESIAN CALIBRATION OF SAFETY CODES USING DATA FROM SEPARATE-AND INTEGRAL EFFECTS TESTS

Large-scale system codes for simulation of safety performance of nuclear plants may contain parameters whose values are not known very accurately. In order to be able to use the results of these simulation codes with confidence, it is important to learn how the uncertainty on the values of these parameters affects the output of the codes. New information from tests or operating experience is incorporated into safety codes by a process known as calibration, which reduces uncertainty in the output of the safety code, and thereby improves its support for decision-making. Modern analysis capabilities afford very significant improvements on classical ways of doing calibration, and the work reported here implements some of those improvements. The key innovation has come from development of safety code surrogate model (code emulator) construction and prediction algorithms. A surrogate is needed for calibration of plant-scale simulation codes because the multivariate nature of the problem (i.e., the need to adjust multiple uncertain parameters at once to fit multiple pieces of new information) calls for multiple evaluations of performance, which, for a computation-intensive model, makes calibration very computation-intensive. Use of a fast surrogate makes the calibration processes used here with Markov Chain Monte Carlo (MCMC) sampling feasible. Moreover, most traditional surrogates do not provide uncertainty information along with their predictions, but the Gaussian Process (GP) based code surrogates used here do. This improves the soundness of the code calibration process. Results are demonstrated on a simplified scenario with data from Separate and Integral Effect Tests.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Automated ICRF heating surrogate modeling via machine learning

This work introduces automated machine learning workflows that address critical bottlenecks in surrogate model development for Ion Cyclotron Range of Frequencies (ICRF) heating applications. The automated framework includes data analysis tools that transform raw datasets into actionable insights in seconds, replacing weeks of manual exploratory effort and ensuring consistent, reproducible dataset characterization. By integrating advanced hyperparameter optimization (HPO) methods including Bayesian optimization via BoTorch and Tree-structured Parzen Estimators (TPE), the framework significantly reduces model development time from weeks to hours, decreasing computational cost and required expertise, while enabling high-accuracy surrogate models. Compared to traditional hyperparameter scanning (HPS) techniques such as methodical, randomized, and grid searches, HPO methods achieve superior convergence and predictive performance, even when compared to already well-tuned reference models. On NSTX High Harmonic Fast Wave (HHFW) heating datasets, both Random Forest Regressor (RFR) and neural network surrogates demonstrate improved accuracy, achieving R 2 values beyond 0.97 and 0.98, respectively. The results show that while HPO gains are modest for robust architectures like RFR, they become essential for more sensitive models such as neural networks, highlighting the trade-offs across optimization strategies. Through automated workflows that eliminate manual hyperparameter tuning and require minimal ML expertise, this work enables widespread adoption of high-fidelity surrogate models across the fusion community for real-time plasma control, uncertainty quantification, rapid experimental scenario development, and integrated system optimization.

Sanchez-Villar, Alvaro [Princeton Plasma Physics L↗
DOE OSTI2024

A differentiable simulation package for performing inference of synchrotron-radiation-based diagnostics

The direction of particle accelerator development is ever-increasing beam quality, currents and repetition rates. This poses a challenge to traditional diagnostics that directly intercept the beam due to the mutual destruction of both the beam and the diagnostic. An alternative approach is to infer beam parameters non-invasively from the synchrotron radiation emitted in bending magnets. However, inferring the beam distribution from a measured radiation pattern is a complex and computationally expensive task. To address this challenge we present SYRIPY ( SYnchrotron Radiation In PYthon ), a software package intended as a tool for performing inference of synchrotron-radiation-based diagnostics. SYRIPY has been developed using PyTorch , which makes it both differentiable and able to leverage the high performance of GPUs, two vital characteristics for performing statistical inference. The package consists of three modules: a particle tracker, Lienard–Wiechert solver and Fourier optics propagator, allowing start-to-end simulation of synchrotron radiation detection to be carried out. SYRIPY has been benchmarked against SRW , the prevalent numerical package in the field, showing good agreement and up to a 50× speed improvement. Finally, we have demonstrated how SYRIPY can be used to perform Bayesian inference of beam parameters using stochastic variational inference.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Towards Compact Neural Networks via End-to-End Training: A Bayesian Tensor Approach with Automatic Rank Determination

Post-training model compression can reduce the inference costs of deep neural networks, but uncompressed training still consumes enormous hardware resources and energy. To enable low-energy training on edge devices, it is highly desirable to directly train a compact neural network from scratch with a low memory cost. Low-rank tensor decomposition is an effective approach to reduce the memory and computing costs of large neural networks. However, directly training low-rank tensorized neural networks is a very challenging task because it is hard to determine a proper tensor rank a priori, and the tensor rank controls both model complexity and accuracy. Here, this paper presents a novel end-to-end framework for low-rank tensorized training. We first develop a Bayesian model that supports various low-rank tensor formats (e.g., CANDECOMP/PARAFAC, Tucker, tensor-train, and tensor-train matrix) and reduces neural network parameters with automatic rank determination during training. Then we develop a customized Bayesian solver to train large-scale tensorized neural networks. Our training methods shows orders-of-magnitude parameter reduction and little accuracy loss (or even better accuracy) in the experiments. On a very large deep learning recommendation system with over 4.2 ×10 9 model parameters, our method can reduce the parameter number to 1.6 ×10 5 automatically in the training process (i.e., by 2.6 ×10 4 times) while achieving almost the same accuracy. Code is available at https://github.com/colehawkins/bayesian-tensor-rank-determination.

compact neural networks↗
DOE OSTI2020

Automation and control of laser wakefield accelerators using Bayesian optimization

Laser wakefield accelerators promise to revolutionize many areas of accelerator science. However, one of the greatest challenges to their widespread adoption is the difficulty in control and optimization of the accelerator outputs due to coupling between input parameters and the dynamic evolution of the accelerating structure. Here, we use machine learning techniques to automate a 100 MeV-scale accelerator, which optimized its outputs by simultaneously varying up to six parameters including the spectral and spatial phase of the laser and the plasma density and length. Most notably, the model built by the algorithm enabled optimization of the laser evolution that might otherwise have been missed in single-variable scans. Subtle tuning of the laser pulse shape caused an 80% increase in electron beam charge, despite the pulse length changing by just 1%.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Probabilistic Nanomagnetic Memories for Uncertain and Robust Machine Learning

This project evaluated the use of emerging spintronic memory devices for robust and efficient variational inference schemes. Variational inference (VI) schemes, which constrain the distribution for each weight to be a Gaussian distribution with a mean and standard deviation, are a tractable method for calculating posterior distributions of weights in a Bayesian neural network such that this neural network can also be trained using the powerful backpropagation algorithm. Our project focuses on domain-wall magnetic tunnel junctions (DW-MTJs), a powerful multi-functional spintronic synapse design that can achieve low power switching while also opening the pathway towards repeatable, analog operation using fabricated notches. Our initial efforts to employ DW-MTJs as an all-in-one stochastic synapse with both a mean and standard deviation didn’t end up meeting the quality metrics for hardware-friendly VI. In the future, new device stacks and methods for expressive anisotropy modification may make this idea still possible. However, as a fall back that immediately satisfies our requirements, we invented and detailed how the combination of a DW-MTJ synapse encoding the mean and a probabilistic Bayes-MTJ device, programmed via a ferroelectric or ionically modifiable layer, can robustly and expressively implement VI. This design includes a physics-informed small circuit model, that was scaled up to perform and demonstrate rigorous uncertainty quantification applications, up to and including small convolutional networks on a grayscale image classification task, and larger (Residual) networks implementing multi-channel image classification. Lastly, as these results and ideas all depend upon the idea of an inference application where weights (spintronic memory states) remain non-volatile, the retention of these synapses for the notched case was further interrogated. These investigations revealed and emphasized the importance of both notch geometry and anisotropy modification in order to further enhance the endurance of written spintronic states. In the near future, these results will be mapped to effective predictions for room temperature and elevated operation DW-MTJ memory retention, and experimentally verified when devices become available.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Data Imbalance, Uncertainty Quantification, and Transfer Learning in Data‐Driven Parameterizations: Lessons From the Emulation of Gravity Wave Momentum Transport in WACCM

Abstract Neural networks (NNs) are increasingly used for data‐driven subgrid‐scale parameterizations in weather and climate models. While NNs are powerful tools for learning complex non‐linear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are (a) data imbalance related to learning rare, often large‐amplitude, samples; (b) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and (c) generalization to other climates, for example, those with different radiative forcings. Here, we examine the performance of methods for addressing these challenges using NN‐based emulators of the Whole Atmosphere Community Climate Model (WACCM) physics‐based gravity wave (GW) parameterizations as a test case. WACCM has complex, state‐of‐the‐art parameterizations for orography‐, convection‐, and front‐driven GWs. Convection‐ and orography‐driven GWs have significant data imbalance due to the absence of convection or orography in most grid points. We address data imbalance using resampling and/or weighted loss functions, enabling the successful emulation of parameterizations for all three sources. We demonstrate that three UQ methods (Bayesian NNs, variational auto‐encoders, and dropouts) provide ensemble spreads that correspond to accuracy during testing, offering criteria for identifying when an NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4 × CO 2 ). However, their performance is significantly improved by applying transfer learning, for example, re‐training only one layer using ∼1% new data from the warmer climate. The findings of this study offer insights for developing reliable and generalizable data‐driven parameterizations for various processes, including (but not limited to) GWs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Deep Learning and Likelihood Approaches for Viral Phylogeography Converge on the Same Answers Whether the Inference Model Is Right or Wrong

Abstract Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models.

Evolutionary Biology↗