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At least 91 records · Page 5

Combination of deep neural network with attention mechanism enhances the explainability of protein contact prediction

Abstract Deep learning has emerged as a revolutionary technology for protein residue‐residue contact prediction since the 2012 CASP10 competition. Considerable advancements in the predictive power of the deep learning‐based contact predictions have been achieved since then. However, little effort has been put into interpreting the black‐box deep learning methods. Algorithms that can interpret the relationship between predicted contact maps and the internal mechanism of the deep learning architectures are needed to explore the essential components of contact inference and improve their explainability. In this study, we present an attention‐based convolutional neural network for protein contact prediction, which consists of two attention mechanism‐based modules: sequence attention and regional attention. Our benchmark results on the CASP13 free‐modeling targets demonstrate that the two attention modules added on top of existing typical deep learning models exhibit a complementary effect that contributes to prediction improvements. More importantly, the inclusion of the attention mechanism provides interpretable patterns that contain useful insights into the key fold‐determining residues in proteins. We expect the attention‐based model can provide a reliable and practically interpretable technique that helps break the current bottlenecks in explaining deep neural networks for contact prediction. The source code of our method is available at https://github.com/jianlin-cheng/InterpretContactMap .

59 BASIC BIOLOGICAL SCIENCES↗

Learning interpretable surface elasticity properties from bulk properties via neural network equation learners

Surface elasticity is central to understanding the mechanics and stability of surfaces and interfaces. It is characterized by quantities such as surface tension, residual surface stress, and surface stiffness. However their analytical expressions are typically difficult to derive from atomistic data, and depend strongly on modeling choices. This work presents a neural network-based equation learner which combines customized activation functions and connection-based pruning to discover parsimonious, closed-form equations for surface elasticity from atomistic simulations. Applying the method to seven face-centered cubic (FCC) metals, our equation learner uncovers interpretable equations that describe both low-Miller index and high-Miller index surface properties, capturing long-tail property distributions accurately. The discovered expressions are decoupled into two components: a universal, geometry-driven orientation function, and material-specific baseline coefficients. We find that lower-order properties such as surface tension are fundamentally geometry dependent, while higher-order properties such as surface stress and elasticity show more complex geometry and material dependence. We also relate material dependent coefficients to bulk properties, forming a clear map from bulk material properties to surface elasticity. Overall, this approach demonstrates that interpretable neurosymbolic machine learning can bridge the gap between atomistic simulations and physical laws, enabling the discovery of generalizable structure–property relationships for materials science phenomena such as surface elasticity.

Equation learning↗

DISTEMA: distance map-based estimation of single protein model accuracy with attentive 2D convolutional neural network

Abstract Background Estimation of the accuracy (quality) of protein structural models is important for both prediction and use of protein structural models. Deep learning methods have been used to integrate protein structure features to predict the quality of protein models. Inter-residue distances are key information for predicting protein’s tertiary structures and therefore have good potentials to predict the quality of protein structural models. However, few methods have been developed to fully take advantage of predicted inter-residue distance maps to estimate the accuracy of a single protein structural model. Result We developed an attentive 2D convolutional neural network (CNN) with channel-wise attention to take only a raw difference map between the inter-residue distance map calculated from a single protein model and the distance map predicted from the protein sequence as input to predict the quality of the model. The network comprises multiple convolutional layers, batch normalization layers, dense layers, and Squeeze-and-Excitation blocks with attention to automatically extract features relevant to protein model quality from the raw input without using any expert-curated features. We evaluated DISTEMA’s capability of selecting the best models for CASP13 targets in terms of ranking loss of GDT-TS score. The ranking loss of DISTEMA is 0.079, lower than several state-of-the-art single-model quality assessment methods. Conclusion This work demonstrates that using raw inter-residue distance information with deep learning can predict the quality of protein structural models reasonably well. DISTEMA is freely at https://github.com/jianlin-cheng/DISTEMA

59 BASIC BIOLOGICAL SCIENCES↗

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .

97 MATHEMATICS AND COMPUTING↗

Informative and non-informative decomposition of turbulent flow fields

Not all the information in a turbulent field is relevant for understanding particular regions or variables in the flow. Here, we present a method for decomposing a source field into its informative Φ I (x, t) and residual Φ R (x, t) components relative to another target field. The method is referred to as informative and non-informative decomposition (IND). All the necessary information for physical understanding, reduced-order modelling and control of the target variable is contained in Φ I (x, t), whereas Φ R (x, t) offers no substantial utility in these contexts. The decomposition is formulated as an optimisation problem that seeks to maximise the time-lagged mutual information of the informative component with the target variable while minimising the mutual information with the residual component. The method is applied to extract the informative and residual components of the velocity field in a turbulent channel flow, using the wall shear stress as the target variable. We demonstrate the utility of IND in three scenarios: (i) physical insight into the effect of the velocity fluctuations on the wall shear stress; (ii) prediction of the wall shear stress using velocities far from the wall; and (iii) development of control strategies for drag reduction in a turbulent channel flow using opposition control. In case (i), IND reveals that the informative velocity related to wall shear stress consists of wall-attached high- and low-velocity streaks, collocated with regions of vertical motions and weak spanwise velocity. This informative structure is embedded within a larger-scale streak–roll structure of residual velocity, which bears no information about the wall shear stress. In case (ii), the best-performing model for predicting wall shear stress is a convolutional neural network that uses the informative component of the velocity as input, while the residual velocity component provides no predictive capabilities. Finally, in case (iii), we demonstrate that the informative component of the wall-normal velocity is closely linked to the observability of the target variable and holds the essential information needed to develop successful control strategies.

97 MATHEMATICS AND COMPUTING↗

Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

Deducing neutron star equation of state from telescope spectra with machine-learning-derived likelihoods

The interiors of neutron stars reach densities and temperatures beyond the limits of terrestrial experiments, providing vital laboratories for probing nuclear physics. While the star's interior is not directly observable, its pressure and density determine the star's macroscopic structure which affects the spectra observed in telescopes. The relationship between the observations and the internal state is complex and partially intractable, presenting difficulties for inference. Previous work has focused on the regression from stellar spectra of parameters describing the internal state. We demonstrate a calculation of the full likelihood of the internal state parameters given observations, accomplished by replacing intractable elements with machine learning models trained on samples of simulated stars. Our machine-learning-derived likelihood allows us to perform maximum a posteriori estimation of the parameters of interest, as well as full scans. We demonstrate the technique by inferring stellar mass and radius from an individual stellar spectrum, as well as equation of state parameters from a set of spectra. Our results are more precise than pure regression models, reducing the width of the parameter residuals by 11.8% in the most realistic scenario. The neural networks will be released as a tool for fast simulation of neutron star properties and observed spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

Fault diagnosis for the Space Shuttle main engine

A conceptual design of a model-based fault detection and diagnosis system is developed for the Space Shuttle main engine. The design approach consists of process modeling, residual generation, and fault detection and diagnosis. The engine is modeled using a discrete time, quasilinear state-space representation. Model parameters are determined by identification. Residuals generated from the model are used by a neural network to detect and diagnose engine component faults. Fault diagnosis is accomplished by training the neural network to recognize the pattern of the respective fault signatures. Preliminary results for a failed valve, generated using a full, nonlinear simulation of the engine, are presented. These results indicate that the developed approach can be used for fault detection and diagnosis. The results also show that the developed model is an accurate and reliable predictor of the highly nonlinear and very complex engine.

Duyar, Ahmet↗

Determining crop residue type and class using satellite acquired data

LANDSAT Thematic Mapper (TM) data for March 23, 1987 with accompanying ground truth data for the study area in Miami County, IN were used to determine crop residue type and class. Principle components and spectral ratioing transformations were applied to the LANDSAT TM data. One graphic information system (GIS) layer of land ownership was added to each original image as the eighth band of data in an attempt to improve classification. Maximum likelihood, minimum distance, and neural networks were used to classify the original, transformed, and GIS-enhanced remotely sensed data. Crop residues could be separated from one another and from bare soil and other biomass. Two types of crop residue and four classes were identified from each LANDSAT TM image. The maximum likelihood classifier performed the best classification for each original image without need of any transformation. The neural network classifier was able to improve the classification by incorporating a GIS-layer of land ownership as an eighth band of data. The maximum likelihood classifier was unable to consider this eighth band of data and thus, its results could not be improved by its consideration.

Zhuang, Xin↗

Research In Nonlinear Flight Control for Tiltrotor Aircraft Operating in the Terminal Area

The research during the first year of the effort focused on the implementation of the recently developed combination of neural net work adaptive control and feedback linearization. At the core of this research is the comprehensive simulation code Generic Tiltrotor Simulator (GTRS) of the XV-15 tilt rotor aircraft. For this research the GTRS code has been ported to a Fortran environment for use on PC. The emphasis of the research is on terminal area approach procedures, including conversion from aircraft to helicopter configuration. This report focuses on the longitudinal control which is the more challenging case for augmentation. Therefore, an attitude command attitude hold (ACAH) control augmentation is considered which is typically used for the pitch channel during approach procedures. To evaluate the performance of the neural network adaptive control architecture it was necessary to develop a set of low order pilot models capable of performing such tasks as, follow desired altitude profiles, follow desired speed profiles, operate on both sides of powercurve, convert, including flaps as well as mastangle changes, operate with different stability and control augmentation system (SCAS) modes. The pilot models are divided in two sets, one for the backside of the powercurve and one for the frontside. These two sets are linearly blended with speed. The mastangle is also scheduled with speed. Different aspects of the proposed architecture for the neural network (NNW) augmented model inversion were also demonstrated. The demonstration involved implementation of a NNW architecture using linearized models from GTRS, including rotor states, to represent the XV-15 at various operating points. The dynamics used for the model inversion were based on the XV-15 operating at 30 Kts, with residualized rotor dynamics, and not including cross coupling between translational and rotational states. The neural network demonstrated ACAH control under various circumstances. Future efforts will include the implementation into the Fortran environment of GTRS, including pilot modeling and NNW augmentation for the lateral channels. These efforts should lead to the development of architectures that will provide for fully automated approach, using similar strategies.

Calise, A. J.↗

Data-Driven Learning of Nonautonomous Systems

In this work, we present a numerical framework for recovering unknown nonautonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the nonautonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗

Moltensaltpropnet

MoltenSaltPropnet is a physics-informed machine learning framework that aims to predict the thermophysical properties of molten fluoride and chloride salt mixtures, which are crucial for the design and safety of Generation IV molten salt reactors. The code processes data from the Molten-Salt Thermal Properties Database (MSTDB-TP) and the Janz compendium, converting critically evaluated correlations into fast, differentiable surrogate models for density, viscosity, thermal conductivity, and heat capacity across 448 distinct salt systems. The implementation consists of several key components: 1. Data Curation: The code parses and cleans the raw data, normalizing elemental mole fractions and extracting relevant regression coefficients for various thermophysical properties. 2. Feature Engineering: It generates fixed-length numerical descriptors that encapsulate the composition and temperature, incorporating polynomial interaction terms and dimensionality-reduction techniques to optimize model performance. 3. Coefficient Learning: Four different machine learning architectures are employed: a deep residual network (ResNet), a Kolmogorov–Arnold network (KAN), a sparsity-inducing neural network (SNN), and classical regression models. Each model learns to predict coefficients that define the temperature-dependent correlations for the thermophysical properties. 4. Property Reconstruction: The predicted coefficients are used to compute temperature-dependent property values, ensuring positivity and monotonic trends through a composite loss function that enforces physical constraints. 5. User Interface: An open-source web application enables users to filter the database, train task-specific models, and visualize the results, allowing for rapid exploration of candidate salt mixtures. MoltenSaltPropnet bridges the gap between limited experimental data and high-fidelity reactor simulations, providing a powerful tool for researchers in the field of molten salt reactors and advanced nuclear energy systems.

Retamales, Mauricio Eduardo Tano [Idaho National L↗

Data-Driven Learning of Non-Autonomous Systems

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗

Cross-reactive immunogenicity of group A streptococcal vaccines designed using a recurrent neural network to identify conserved M protein linear epitopes

The M protein of group A streptococci (Strep A) is a major virulence determinant and protective antigen. The N-terminal sequence of the protein defines the more than 200 M types of Strep A and also contains epitopes that elicit opsonic antibodies, some of which cross-react with heterologous M types. Current efforts to develop broadly protective M protein-based vaccines are directed at identifying potential cross-protective epitopes located in the N-terminal regions of cluster-related M proteins for use as vaccine antigens. In this study, we have used a comprehensive approach using the recurrent neural network ABCpred and IEDB epitope conservancy analysis tools to predict 16 residue linear B-cell epitopes from 117 clinically relevant M types of Strep A (~88% of global Strep A infections). Furthermore, to examine the immunogenicity of these epitope-based vaccines, nine peptides that together shared ≥60% sequence identity with 37 heterologous M proteins were incorporated into two recombinant hybrid protein vaccines, in which the epitopes were repeated 2 or 3 times, respectively. The combined immune responses of immunized rabbits showed that the vaccines elicited significant levels of antibodies against all nine vaccine epitopes present in homologous N-terminal 1–50 amino acid synthetic M peptides, as well as cross-reactive antibodies against 16 of 37 heterologous M peptides predicted to contain similar epitopes. The epitope-specificity of the cross-reactive antibodies was confirmed by ELISA inhibition assays and functional opsonic activity was assayed in HL-60-based bactericidal assays. The results provide important information for the future design of broadly protective M protein-based Strep A vaccines.

60 APPLIED LIFE SCIENCES↗

Photometric redshift estimation with convolutional neural networks and galaxy images: Case study of resolving biases in data-driven methods

Deep-learning models have been increasingly exploited in astrophysical studies, but these data-driven algorithms are prone to producing biased outputs that are detrimental for subsequent analyses. In this work, we investigate two main forms of biases: class-dependent residuals, and mode collapse. We do this in a case study, in which we estimate photometric redshift as a classification problem using convolutional neural networks (CNNs) trained with galaxy images and associated spectroscopic redshifts. We focus on point estimates and propose a set of consecutive steps for resolving the two biases based on CNN models, involving representation learning with multichannel outputs, balancing the training data, and leveraging soft labels. The residuals can be viewed as a function of spectroscopic redshift or photometric redshift, and the biases with respect to these two definitions are incompatible and should be treated individually. We suggest that a prerequisite for resolving biases in photometric space is resolving biases in spectroscopic space. Experiments show that our methods can better control biases than benchmark methods, and they are robust in various implementing and training conditions with high-quality data. Our methods hold promises for future cosmological surveys that require a good constraint of biases, and they may be applied to regression problems and other studies that make use of data-driven models. Nonetheless, the bias-variance tradeoff and the requirement of sufficient statistics suggest that we need better methods and optimized data usage strategies.

79 ASTRONOMY AND ASTROPHYSICS↗

Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches

Abstract In complex systems with multiple variables monitored at high‐frequency, variables are not only temporally autocorrelated, but they may also be nonlinearly related or exhibit nonstationarity as the inputs or operation changes. One approach to handling such variables is to detrend them prior to monitoring and then apply control charts that assume independence and stationarity to the residuals. Monitoring controlled systems is even more challenging because the control strategy seeks to maintain variables at prespecified mean levels, and to compensate, correlations among variables may change, making monitoring the covariance essential. In this paper, a vector autoregressive model (VAR) is compared with a multivariate random forest (MRF) and a neural network (NN) for detrending multivariate time series prior to monitoring the covariance of the residuals using a multivariate exponentially weighted moving average (MEWMA) control chart. Machine learning models have an advantage when the data's structure is unknown or may change. We design a novel simulation study with nonlinear, nonstationary, and autocorrelated data to compare the different detrending models and subsequent covariance monitoring. The machine learning models have superior performance for nonlinear and strongly autocorrelated data and similar performance for linear data. An illustration with data from a reverse osmosis process is given.

Weix, Derek↗

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗

The Impact and Estimation of Uncertainty Correlation for Multi-Angle Polarimetric Remote Sensing of Aerosols and Ocean Color

Multi-angle polarimetric (MAP) measurements contain rich information for characterization of aerosol microphysical and optical properties that can be used to improve atmospheric correction in ocean color remote sensing. Advanced retrieval algorithms have been developed to obtain multiple geophysical parameters in the atmosphere-ocean system, although uncertainty correlation among measurements is generally ignored due to lack of knowledge on its strength and characterization. In this work, we provide a practical framework to evaluate the impact of the angular uncertainty correlation from retrieval results and a method to estimate correlation strength from retrieval fitting residuals. The Fast Multi-Angular Polarimetric Ocean coLor (FastMAPOL) retrieval algorithm, based on neural network forward models, is used to conduct the retrievals and uncertainty quantification. In addition, we also discuss a flexible approach to include a correlated uncertainty model in the retrieval algorithm. The impact of angular correlation on retrieval uncertainties is discussed based on synthetic AirHARP and HARP2 measurements using a Monte Carlo uncertainty estimation method. Correlation properties are estimated using auto-correlation functions based on the fitting residuals from both synthetic AirHARP and HARP2 data and real AirHARP measurement, with the resulting angular correlation parameters found to be larger than 0.9 and 0.8 for reflectance and DoLP, respectively, which correspond to correlation angles of 10° and 5°. Although this study focuses on angular correlation from HARP instruments, the methodology to study and quantify uncertainty correlation is also applicable to other instruments with angular, spectral, or spatial correlations, and can help inform laboratory calibration and characterization of the instrument uncertainty structure.

PACE↗