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Despite an ever-growing number of data sets that catalog and characterize interactions between microbes in different environments and conditions, many of these data are neither easily accessible nor intercompatible. These limitations present a major challenge to microbiome research by hindering the streamlined drawing of inferences across studies.
Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a novel stability analysis method and provide sufficient conditions of DMM's stochastic stability. The proposed stability analysis is based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation function on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.
Scanning electron microscopy (SEM) is resource intensive, which limits its throughput in some applications. As an alternative, we propose applying computer vision and machine learning to generate high-quality synthetic SEM micrographs from micrographs obtained using light optical microscopy (LOM). Working with a correlated LOM/SEM dataset of dual-phase steel images, we test generative models of various architectures, including encoder-decoder networks, generative adversarial networks (GANs), and diffusion-based models. We find that the diffusion models significantly outperform other methods on both qualitative and quantitative assessments, while preserving key metallurgical meaning. This work establishes diffusion as the state-of-the-art for microscopy modality transfer and demonstrates the potential of AI-powered microscopy to enhance LOM with micron scale structural recreation.
The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians and others have long been interested in this problem, which has led to several practical and innovative solutions dating back decades. In this overview, we focus on the problem of data-driven prediction and inference of dynamic spatio-temporal processes that include mechanistic information, such as would be available from partial differential equations, with a strong focus on the quantification of uncertainty associated with data, process, and parameters. Here, we give a brief review of several paradigms and focus our attention on Bayesian implementations given they naturally accommodate uncertainty quantification. We then show that it is straight-forward to include the Bayesian PINN (B-PINN) within the Bayesian hierarchical model (BHM) framework that has long been considered for modeling dynamic spatio-temporal processes. Such a BHM-PINN is illustrated via a simulation study in which a latent nonlinear Burgers’ equation PDE governs the dynamics of Poisson distributed spatio-temporal data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
The resilience of safety-critical systems is gaining importance due to the rise in cyber and physical threats, especially within critical infrastructure. Traditional static resilience metrics may not capture dynamic system states, leading to inaccurate assessments and ineffective responses to cyber threats. This work aims to develop a data-driven, adaptive method for resilience metric learning. We propose a data-driven approach using inverse reinforcement learning (IRL) to learn a single, adaptive resilience metric. The method infers a reward function from expert control actions. Unlike previous approaches using static weights or fuzzy logic, this work applies adversarial inverse reinforcement learning (AIRL), training a generator and discriminator in parallel to learn the reward structure and derive an optimal policy. The proposed approach is evaluated on multiple scenarios: optimal communication network rerouting, power distribution network reconfiguration, and cyber–physical restoration of critical loads using the IEEE 123-bus system. The adaptive, learned resilience metric enables faster critical load restoration in comparison to conventional RL approaches.
A method for digital image segmentation is provided. The method comprises training a neural network for image segmentation with a labeled training dataset from a first domain, wherein a subset of nodes in the neural net are dropped out during training. The neural network receives image data from a second, different domain. A vector of N values that sum to 1 is calculated for each image element, wherein each value represents an image segmentation class. A label is assigned to each image element according to the class with the highest value in the vector. Multiple inferences are performed with active dropout layers for each image element, and an uncertainty value is generated for each image element. The label of any image element with an uncertainty value above a predefined threshold is replaced with a new label corresponding to the class with the next highest value.
Digital image segmentation is provided. The method comprises training a neural network for image segmentation with a labeled training dataset from a first domain, wherein a subset of nodes in the neural net are dropped out during training. The neural network receives image data from a second, different domain. A vector of N values that sum to 1 is calculated for each image element, wherein each value represents an image segmentation class. A label is assigned to each image element according to the class with the highest value in the vector. Multiple inferences are performed with active dropout layers for each image element, and an uncertainty value is generated for each image element. Uncertainty is resolved according to expected characteristics. The label of any image element with an uncertainty above a threshold is replaced with a new label corresponding to a segmentation class based on domain knowledge.
We present cosmological constraints from the Dark Energy Survey Year 3 (DES Y3) weak lensing data using hierarchical hybrid statistics within a Bayesian simulation-based inference framework that is based on the Gower Street simulations. To maximize the precision of the inference, we have developed a new, information-theory based, data compression of the weak lensing maps to just seven highly informative summary statistics. The hybrid scheme exploits the high information content of the power spectrum, compressing both the power spectrum and neural-based summaries that are designed to extract further information. Our simulation-based approach enables principled forward modelling of all major sources of systematic uncertainty and survey properties into realistic mock observations, including the survey mask, photometric redshift uncertainties, intrinsic galaxy alignments, multiplicative shear calibration bias, source galaxy clustering, non-Gaussian shape noise, and non-linear structure formation. The summary statistics are then used in a Bayesian simulation-based inference pipeline. The inference is validated through coverage tests and checks for robustness against baryonic feedback. Assuming a $w$CDM cosmology, our analysis yields $S_8 = 0.808 \pm 0.017$, $Ω_{\rm m} = 0.325 \pm 0.024$, and $w < -0.766$ (marginalized posterior 68 per cent credible intervals). This rigorous combination of information theory, physics- and neural network-based extreme data compression, and principled Bayesian analysis improves the figure of merit for $(Ω_{\rm m}, S_8, w)$ by 60 per cent over the previous state-of-the-art, and by almost a factor of 3 over two-point analyses of the same data. They are the most precise joint constraints on $(Ω_{\rm m}, S_8, w)$ from weak gravitational lensing data alone of any survey to date. We intend to apply this analysis to the more recent DES Y6 data.
Fully hadronic \(t\bar{t}\) reconstruction requires assigning reconstructed jets to the two top-quark decay branches, \(t\bar{t}\to(Wb)(Wb)\to(qqb)(qqb)\). This is a combinatorially large, symmetry-rich, and frequently underconstrained set-assignment problem due to detector effects and partial reconstructability. SPANet provides a strong symmetry-preserving baseline for this task, but its standard inference eagerly commits to a single hypothesis and does not explicitly treat branch-level reconstructability decisions. We present a two-stage extension of the SPANet pipeline for fully hadronic \(t\bar{t}\) events: (i) SPANet is modified into a proposal model that generates a shortlist of candidate jet assignments; (ii) a custom dual-head set transformer is trained to re-rank these candidates and identify reconstructible branches. Our extension gives modest improvements in candidate-selection efficiency, with SPANet achieving \(69.9\%\) and our extension achieving \(71.1\%\). Finally, an oracle study of the generated shortlist shows a substantial upper bound of \(88.5\%\) on the evaluated fully reconstructable subset, suggesting that the shortlist contains significant residual information that is not fully exploited.
Our modern understanding of cosmological structure formation posits that small matter density fluctuations present in the early Universe, as traced by the cosmic microwave background, grow via gravitational instability to form extended haloes of dark matter. A theoretical understanding of the structure, evolution and formation of dark matter haloes is an essential step towards unravelling the intricate connection between halo and galaxy formation, needed to test our cosmological model against data from upcoming galaxy surveys. Physical understanding of the process of dark matter halo formation is made difficult by the highly non-linear nature of the haloes' evolution. I describe a new approach to gain physical insight into cosmological structure formation based on machine learning. This approach combines the ability of machine learning algorithms to learn non-linear relationships, with techniques that enable us to physically interpret the learnt mapping. I describe applicatio ns of th e method, with the aim of investigating which aspects of the early universe density field impact the later formation of dark matter haloes. First I present a case where the process of halo formation is turned into a binary classification problem; the algorithm predicts whether or not dark matter `particles' in the initial conditions of a simulation will collapse into haloes of a given mass range. Second, I present its generalization to regression, where the algorithm infers the final mass of the halo to which each particle will later belong. I show that the initial tidal shear does not play a significant role compared to the initial density field in establishing final halo masses. Finally, I demonstrate that extending the framework to deep learning algorithms such as convolutional neural networks allows us to explore connections between the early universe and late time haloes beyond those studied by existing analytic approximations of halo collapse.
Representing complex systems as graphs enables use of mathematical tools to identify faults or predict failures. Graph nodes correspond to individual modules or subsystems, and edges link coupled system parts. ‘Probes’ measure the node outputs, monitoring the system health for unexpected behavior. Assuming one cannot probe every point, within a system, the fault correlates to a region—not necessarily the specific location. Bayesian networks trained to understand fault patterns can accurately identify the source. The diagnostic tool described aides debugging by pinpointing system failure causes. For predictive maintenance, probe data develop probability distribution functions describing subsystem mean time to failure. Unit lifetime can be estimated through these probability distributions. Two approaches include using Bayesian classifiers to infer the system failure source and developing maintenance schedules by treating systems as collections of random variables. When failure behavior does not follow a closed form function, use of similarity models is proposed.
We introduce EFIT-Prime, a novel machine learning surrogate model for EFIT (Equilibrium FIT) that integrates probabilistic and physics-informed methodologies to overcome typical limitations associated with deterministic and ad hoc neural network architectures. EFIT-Prime utilizes a neural architecture search-based deep ensemble for robust uncertainty quantification, providing scalable and efficient neural architectures that comprehensively quantify both data and model uncertainties. Physically informed by the Grad–Shafranov equation, EFIT-Prime applies a constraint on the current density J tor and a smoothness constraint on the first derivative of the poloidal flux, ensuring physically plausible solutions. Furthermore, the spatial location of the diagnostics is explicitly incorporated in the inputs to account for their spatial correlation. Extensive evaluations demonstrate EFIT-Prime's accuracy and robustness across diverse scenarios, most notably showing good generalization on negative-triangularity discharges that were excluded from training. Timing studies indicate an ensemble inference time of 15 ms for predicting a new equilibrium, offering the possibility of plasma control in real-time, if the model is optimized for speed.
We performed large-scale molecular dynamics simulations based on a machine-learning force field (MLFF) to investigate the Li-ion transport mechanism in cation-disordered Li 3 TiCl 6 cathode at six different temperatures, ranging from 25°C to 100°C. In this work, deep neural network method and data generated by ab − initio molecular dynamics (AIMD) simulations were deployed to build a high-fidelity MLFF. Radial distribution functions, Li-ion mean square displacements (MSD), diffusion coefficients, ionic conductivity, activation energy, and crystallographic direction-dependent migration barriers were calculated and compared with corresponding AIMD and experimental data to benchmark the accuracy of the MLFF. From MSD analysis, we captured both the self and distinct parts of Li-ion dynamics. The latter reveals that the Li-ions are involved in anti-correlation motion that was rarely reported for solid-state materials. Similarly, the self and distinct parts of Li-ion dynamics were used to determine Haven’s ratio to describe the Li-ion transport mechanism in Li 3 TiCl 6 . Obtained trajectory from molecular dynamics infers that the Li-ion transportation is mainly through interstitial hopping which was confirmed by intra- and inter-layer Li-ion displacement with respect to simulation time. Ionic conductivity (1.06 mS/cm) and activation energy (0.29eV) calculated by our simulation are highly comparable with that of experimental values. Overall, the combination of machine-learning methods and AIMD simulations explains the intricate electrochemical properties of the Li 3 TiCl 6 cathode with remarkably reduced computational time. Thus, our work strongly suggests that the deep neural network-based MLFF could be a promising method for large-scale complex materials.
Recently, recurrent deep networks have shown promise to harness newly available satellite–sensed data for long–term soil moisture projections. However, to be useful in forecasting, deep networks must also provide uncertainty estimates. Here we evaluated Monte Carlo dropout with an input–dependent data noise term (MCD+N), an efficient uncertainty estimation framework originally developed in computer vision, for hydrologic time series predictions. MCD+N simultaneously estimates a heteroscedastic input–dependent data noise term (a trained error model attributable to observational noise) and a network weight uncertainty term (attributable to insufficiently constrained model parameters). Although MCD+N has appealing features, many heuristic approximations were employed during its derivation, and rigorous evaluations and evidence of its asserted capability to detect dissimilarity were lacking. To address this, we provided an in–depth evaluation of the scheme's potential and limitations. We showed that for reproducing soil moisture dynamics recorded by the Soil Moisture Active Passive (SMAP) mission, MCD+N indeed gave a good estimate of predictive error, provided that we tuned a hyperparameter and used a representative training data set. The input–dependent term responded strongly to observational noise, while the model term clearly acted as a detector for physiographic dissimilarity from the training data, behaving as intended. However, when the training and test data were characteristically different, the input–dependent term could be misled, undermining its reliability. Additionally, due to the data–driven nature of the model, data noise also influences network weight uncertainty, and therefore the two uncertainty terms are correlated. Altogether, this approach has promise, but care is needed to interpret the results.
Capturing the structural changes that molecules undergo during chemical reactions in real space and time is a long-standing dream and an essential prerequisite for understanding and ultimately controlling femtochemistry. A key approach to tackle this challenging task is Coulomb explosion imaging, which benefited decisively from recently emerging high-repetition-rate X-ray free-electron laser sources. With this technique, information on the molecular structure is inferred from the momentum distributions of the ions produced by the rapid Coulomb explosion of molecules. Retrieving molecular structures from these distributions poses a highly non-linear inverse problem that remains unsolved for molecules consisting of more than a few atoms. Here, we address this challenge using a diffusion-based Transformer neural network. We show that the network reconstructs unknown molecular geometries from ion-momentum distributions with a mean absolute error below one Bohr radius, which is half the length of a typical chemical bond.
Water under nanoconfinement at ambient conditions has exhibited low-dimensional ice formation and liquid–solid phase transitions, but with structural and dynamical signatures that map onto known regions of water’s phase diagram. Using terahertz (THz) absorption spectroscopy and ab initio molecular dynamics, we have investigated the ambient water confined in a supramolecular tetrahedral assembly, and determined that a dynamically distinct network of 9 ± 1 water molecules is present within the nanocavity of the host. The low-frequency absorption spectrum and theoretical analysis of the water in the Ga 4 L 6 12– host demonstrate that the structure and dynamics of the encapsulated droplet is distinct from any known phase of water. A further inference is that the release of the highly unusual encapsulated water droplet creates a strong thermodynamic driver for the high-affinity binding of guests in aqueous solution for the Ga 4 L 6 12– supramolecular construct.
Stress is not uniform in the Earth. Therefore, we must use natural experiments to measure the distribution of stresses and related quantities, rather than single values. For instance, dynamic triggering shows that faults are uniformly distributed over their loading cycles in Southern California. The probability that a fault ruptures across a barrier measures the in situ energy distribution. Fault roughness reflects the distribution of strength. These natural experiments produce observable distributions that are surprisingly consistent and suggest some degree of self-organization in the Earth’s crust. Once established, the functional form of the distributions can be used to track changes in response to earthquakes as well as to distinguish fundamentally different fault systems. Transient fault locking before stress release in laboratory experiments can be interpreted as a consequence of self-organization of fault stress. The robust self-organization of multiple variables in earthquake systems suggests that the most consequential mechanical outcome of earthquakes may be the redistribution of stress and the strain energy associated with it. The low friction on a fault during seismic slip as inferred by temperature measurements of the Tohoku earthquake is consistent with dissipation playing a secondary role to this redistribution process. Through stress redistribution and interaction, subduction zone faults tend to synchronize, perhaps due to their geometric simplicity, while the continental system of Southern California cannot synchronize, perhaps due to the complexity of the fault network. Earthquakes organize stress in the crust and produce a suite of well-defined, consistent distributions.
A surrogate model of the runaway electron avalanche growth rate in a magnetic fusion plasma is developed. This is accomplished by employing a physics-informed neural network (PINN) to learn the parametric solution of the adjoint to the relativistic Fokker–Planck equation. The resulting PINN is able to evaluate the runaway probability function across a broad range of parameters in the absence of any synthetic or experimental data. This surrogate of the adjoint relativistic Fokker–Planck equation is then used to infer the avalanche growth rate as a function of the electric field, synchrotron radiation and effective charge. Predictions of the avalanche PINN are compared against first principle calculations of the avalanche growth rate with excellent agreement observed across a broad range of parameters.