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At least 91 records · Page 5

Scientific Discovery with Physics-Informed System Identification (Abbreviated Report)

My fellowship research focused on making physics-based simulations faster and more useful through machine learning. Many problems in science and engineering are governed by partial differential equations, but high-fidelity simulations are often too expensive to run repeatedly. I worked on improving Latent Space Dynamics Identification (LaSDI), a reduced-order modeling framework that compresses large simulation data sets into a smaller representation and then learns how that representation evolves over time. The motivation was to develop reduced models that remain accurate for more challenging systems, especially when predictions must remain reliable over long time intervals or when the underlying dynamics are more complicated than standard methods can easily handle. I also contributed to related work on Quandary, a high-performance software effort for simulation and control of open quantum systems, before focusing primarily on Latent Space Dynamics Identification methods. The main outcomes of the fellowship were two new algorithms (both of which were published), Rollout-LaSDI and Higher-Order LaSDI, together with supporting work on multi-stage Latent Space Dynamics Identification. Rollout-LaSDI improved long-term prediction by training the model to stay accurate over extended time horizons, and Higher-Order LaSDI broadened the method so it could model systems with higher-order time dynamics. My contributions to multistage Latent Space Dynamics Identification also helped show that its later training stages could be simplified without losing effectiveness, and that this behavior held across different model architectures and training strategies. Taken together, these advances improved the accuracy, flexibility, and practical value of reduced-order modeling tools for computational science.

97 MATHEMATICS AND COMPUTING↗

Predicting fault slip via transfer learning

Abstract Data-driven machine-learning for predicting instantaneous and future fault-slip in laboratory experiments has recently progressed markedly, primarily due to large training data sets. In Earth however, earthquake interevent times range from 10’s-100’s of years and geophysical data typically exist for only a portion of an earthquake cycle. Sparse data presents a serious challenge to training machine learning models for predicting fault slip in Earth. Here we describe a transfer learning approach using numerical simulations to train a convolutional encoder-decoder that predicts fault-slip behavior in laboratory experiments. The model learns a mapping between acoustic emission and fault friction histories from numerical simulations, and generalizes to produce accurate predictions of laboratory fault friction. Notably, the predictions improve by further training the model latent space using only a portion of data from a single laboratory earthquake-cycle. The transfer learning results elucidate the potential of using models trained on numerical simulations and fine-tuned with small geophysical data sets for potential applications to faults in Earth.

58 GEOSCIENCES↗

A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.

Computational Engineering, Finance, and Science (c↗

Learning Latent Representations to Bridge Coarse-Grained and Atomistic Resolutions in Polymer Simulations

We present a machine-learning-based framework for learning reduced-order representations of polymer chain conformations across coarse-grained (CG) and united-atom (UA) fidelities. By employing linear singular value decomposition and nonlinear autoencoders, we compress high-dimensional polymer configurations into latent spaces with minimal loss of structural accuracy. Crucially, we demonstrate a near-perfect linear mapping between CG and UA latent spaces, enabling an efficient super-resolution back-mapping procedure that reconstructs high-fidelity UA configurations from CG simulations. While minor structural inaccuracies occur, they are effectively corrected through a brief molecular dynamics relaxation, forming a practical hybrid machine learning−physics scheme. This approach establishes the key structural prerequisites for accelerated polymer dynamics simulations: a compact and accurate latent encoding of polymer chain conformations and a validated multi-fidelity mapping that permits reconstruction of UA structures from CG configurations. The extension of this framework to explicit time evolution within the latent space, enabling dynamics to be propagated at CG fidelity and decoded to UA resolution only when required, represents a natural and well-motivated direction for future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Self-supervised learning of spatiotemporal thermal signatures in additive manufacturing using reduced order physics models and transformers

Microstructure control via additive manufacturing has enormous potential as manufacturers, materials scientists, and designers alike seek to exploit novel fabrication technologies to improve component performance. Recent works have demonstrated the feasibility of producing materials with controlled microstructures across various length scales. However, the experimental approach towards exploring the process-structure space can be laborious and costly. This is particularly true if also considering scan pattern optimization which is well suited for processes such as powder bed fusion electron beam melting. In this work we propose an approach for encoding additive manufacturing layer-wise thermal response signatures using self-supervised representation learning. Thermal simulations from a reduced order model are utilized to estimate the spatiotemporal response during printing. A machine learning framework, using video-transformers, is utilized to efficiently distill spatiotemporal patterns into a compact latent space representation. This latent state representation encodes the relevant physics which is then utilized to establish a data-driven process-structure model for an additively manufactured Ni-based superalloy. In conclusion, the proposed methodology could potentially be used towards in-situ process monitoring, scan pattern experimental design, and component qualification.

97 MATHEMATICS AND COMPUTING↗

Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning

Abstract We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC–AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT–AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. We illustrate that a proficient construction of the latent space is key to achieving these results, enabling us to map these latent spaces using regression models. The proposed framework achieves a relative error of 2% on average and 12% in the worst-case scenario (i.e., the training data is small, but the parameter space is large.). We also show that our framework provides a speed-up of $$7 \times 10^{6}$$ 7 × 10 6 times, in the best case, and $$7 \times 10^{3}$$ 7 × 10 3 times on average compared to a finite element solver. Furthermore, this BT–AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.

97 MATHEMATICS AND COMPUTING↗

Multiscale graph neural network autoencoders for interpretable scientific machine learning

The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes. This is accomplished here with the development of a novel graph neural network (GNN) autoencoding architecture with demonstrations on complex fluid flow applications. To address the first goal of interpretability, the GNN autoencoder achieves reduction in the number nodes in the encoding stage through an adaptive graph reduction procedure. Further, this reduction procedure essentially amounts to flowfieldconditioned node sampling and sensor identification, and produces interpretable latent graph representations tailored to the flowfield reconstruction task in the form of so-called masked fields. These masked fields allow the user to (a) visualize where in physical space a given latent graph is active, and (b) interpret the time-evolution of the latent graph connectivity in accordance with the time-evolution of unsteady flow features (e.g. recirculation zones, shear layers) in the domain. To address the goal of unstructured mesh compatibility, the autoencoding architecture utilizes a series of multi-scale message passing (MMP) layers, each of which models information exchange among node neighborhoods at various lengthscales. The MMP layer, which augments standard single-scale message passing with learnable coarsening operations, allows the decoder to more efficiently reconstruct the flowfield from the identified regions in the masked fields. Analysis of latent graphs produced by the autoencoder for various model settings are conducted using unstructured snapshot data sourced from large-eddy simulations in a backward-facing step (BFS) flow configuration with an OpenFOAM-based flow solver at high Reynolds numbers.

97 MATHEMATICS AND COMPUTING↗

ML-based Dimension Reduction Strategies

Deep learning (DL)--based surrogate models have achieved success in various applications in carbon capture and storage (CCS). However, the model training on high-dimensional spaces is computationally expensive and impractical for large-scale and complex geological models, because the models usually contain hundreds of thousands to millions of grid cells, each with a set of parameters. Furthermore, the high cost of generating training data with sufficient variation is another limitation of model training on high-dimensional spaces, which may result in overfitting and reduce the model efficiency and prediction performance. We proposed the workflow incorporating dimension reduction methods and deep learning models, which aim to extract the latent variables of input parameters and output state variables, and then build the mapping function at the latent spaces. The proposed workflow can significantly reduce the computational complexity in solving both forward and inverse problems compared to models trained on high-dimensional spaces. Dimensionality reduction models showed great potential in workflows for fast reservoir simulation, history matching, prior model generation, visualization, and more, ultimately enhancing DL model performance in related SMART Work Packages.

Hosseini, Seyyed↗

Enhancing Unknown Waveform Detection by Learning Intra and Inter-domain Dependencies with Advanced Attention Fusion Mechanisms

Detection of unknown waveforms in mission-critical communications is a crucial area of interest for the Department of Energy (DoE). Traditional methods and recent deep learning-based approaches often assume that the training set includes all possible classes, which is impractical for detecting new waveforms. This limitation gives rise to the problem of open-set recognition (OSR), which involves correctly identifying known classes while detecting and rejecting unknown or unseen classes. To address this limitation, we propose a novel dual-domain complex-valued neural architecture that jointly processes time-domain and frequency-domain signal representations using transformer mechanisms. A transformer model is a deep learning architecture that uses self-attention mechanisms to process and learn relationships in sequential data. Our model employs a cosine similarity loss to extract domain-specific features and incorporates a transformer architecture in the latent space to weigh the importance of different features from the time and frequency domains. The transformer layer includes stacked self-attention and cross-attention modules to learn intra-domain and inter-domain dependencies, creating a more holistic signal representation. An attention-based fusion module intelligently combines the time and frequency-domain features using multi-head attention, enabling the network to learn the optimal feature for each domain in each input signal. Quantitative results demonstrate the impact of these architectural choices on overall performance, showing significant improvement after incorporating self and cross-attention modules and using complex attention fusion over simple weighted fusion. Our ongoing work will focus on addressing the limitations of threshold-based OSR methods by developing a novel generative framework that integrates a conditional diffusion probabilistic model (DPM). DPM is a generative framework that learns to synthesize complex data by reversing a gradual noising process using a neural network trained to denoise step-by-step. Our goal is to leverage the inherent strengths of DPMs for identifying unknown signals more robustly. One primary advantage of using a DPM is its ability to provide a more reliable anomaly score based on the model's reconstruction error, rather than relying solely on classifier confidence. Additionally, the iterative denoising process of DPMs makes this approach naturally resilient to low Signal-to-Noise Ratio (SNR) conditions, where traditional methods often fail. By implementing this generative framework, we aim to enhance the model's capability to accurately detect unknown waveforms and maintain performance in challenging environments.

99 - GENERAL AND MISCELLANEOUS↗

Real-time tracking of structural evolution in 2D MXenes using theory-enhanced machine learning

In situ Electron Energy Loss Spectroscopy (EELS) combined with Transmission Electron Microscopy (TEM) has traditionally been pivotal for understanding how material processing choices affect local structure and composition. However, the ability to monitor and respond to ultrafast transient changes, now achievable with EELS and TEM, necessitates innovative analytical frameworks. Here, we introduce a machine learning (ML) framework tailored for the real-time assessment and characterization of in operando EELS Spectrum Images (EELS-SI). We focus on 2D MXenes as the sample material system, specifically targeting the understanding and control of their atomic-scale structural transformations that critically influence their electronic and optical properties. This approach requires fewer labeled training data points than typical deep learning classification methods. By integrating computationally generated structures of MXenes and experimental datasets into a unified latent space using Variational Autoencoders (VAE) in a unique training method, our framework accurately predicts structural evolutions at latencies pertinent to closed-loop processing within the TEM. This study presents a critical advancement in enabling automated, on-the-fly synthesis and characterization, significantly enhancing capabilities for materials discovery and the precision engineering of functional materials at the atomic scale.

47 OTHER INSTRUMENTATION↗

Cartesian equivariant representations for learning and understanding molecular orbitals

Qualitative and quantitative orbital properties such as bonding/antibonding character, localization, and orbital energies are critical to how chemists understand reactivity, catalysis, and excited-state behavior. Despite this, representations of orbitals in deep learning models have been very underdeveloped relative to representations of molecular geometries and Hamiltonians. Here, we apply state-of-the-art equivariant deep learning architectures to the task of assigning global labels to orbitals, namely energies characterizations, given the molecular coefficients from Hartree–Fock or density functional theory. The architecture we have developed, the Cartesian Equivariant Orbital Network (CEONET), shows how molecular orbital coefficients are readily featurized as equivariant node features common to all graph-based machine-learned potentials. We find that CEONET performs well at predicting difficult quantitative labels such as the orbital energy and orbital entropy. Furthermore, we find that the CEONET representation provides an intuitive latent space for differentiating orbital character for the qualitative assignment of e.g. bonding or antibonding character. In addition to providing a useful representation for further integrating deep learning with electronic structure theory, we expect CEONET to be useful for automatizing and interpreting the results of advanced electronic structure methods such as complete active space self-consistent field theory. In particular, the ability of CEONET to infer multireference character via the orbital entropy paves the way toward the machine-learned selection of active spaces.

chemical reactions↗

Active deep kernel learning of molecular properties from structural embeddings

As vast databases of chemical identities become increasingly available, the challenge shifts to how we effectively explore and leverage these resources to study molecular properties. This paper presents an active learning approach for molecular discovery using deep kernel learning (DKL), demonstrated on the QM9 dataset. DKL links structural embeddings directly to properties, creating organized latent spaces that prioritize relevant property information. By iteratively recalculating embedding vectors in alignment with target properties, DKL uncovers concentrated maxima representing key molecular properties and reveals unexplored regions with potential for innovation. This approach underscores DKL’s potential in advancing molecular research and discovery.

Artificial neural networks↗

Latent-Space Dynamics for Prediction and Fault Detection in Geothermal Power Plant Operations

This paper presents a latent-space dynamic neural network (LSDNN) model for the multi-step-ahead prediction and fault detection of a geothermal power plant’s operation. The model was trained to learn the dynamics of the power generation process from multivariate time-series data and the effects of exogenous variables, such as control adjustment and ambient temperature. In the LSDNN model, an encoder–decoder architecture was designed to capture cross-correlation among different measured variables. In addition, a latent space dynamic structure was proposed to propagate the dynamics in the latent space to enable prediction. The prediction power of the LSDNN was utilized for monitoring a geothermal power plant and detecting abnormal events. The model was integrated with principal component analysis (PCA)-based process monitoring techniques to develop a fault-detection procedure. The performance of the proposed LSDNN model and fault detection approach was demonstrated using field data collected from a geothermal power plant.

15 GEOTHERMAL ENERGY↗

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

tLaSDI: Thermodynamics-informed latent space dynamics identification

Here we propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

97 MATHEMATICS AND COMPUTING↗

Thermodynamics-informed latent space dynamics identification

This software showcases a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

Cheung, Siu Wun↗

Quantum-Assisted Variational Segmentation for Image-to-Image Wildfire Detection Using Satellite Data

The quantum computing community has been searching for suitable applications to demonstrate the potential of near-term quantum devices. Quantum machine learning is a potential candidate, particularly using models that cannot be efficiently simulated with classical computers [1, 2]. This work focuses on a transition phase of quantum computers where the quantum machine learning model is still simulable classically but projected not to be simulable as the size of the model grows. Ultimately quantum computers may have advantages for high-dimensional real-world problems. Due to the limited number of qubits in current noisy intermediate-scale quantum (NISQ) devices, the direct application of quantum computers in high dimensional data is not feasible. To remedy this problem, an encoder-decoder architecture can be utilized. The encoder model would transform the high-dimensional data into a compact representation, to a level that small quantum computers can be used today (or in the near future), and the decoder would take the quantum processed outputs back to the high-dimensional space. Addressing the two challenges of quantum machine learning, this work investigates a hybrid supervised generative model with a quantum Ising Born machine embedded as the latent distribution. The model contains four main parts (Figure 1.a.): (1) a U-NET architecture responsible for learning segmentation flow, (2) a Prior network responsible for learning an encoded latent distribution of the input data, (3) a Born machine which represents the latent distribution, and (4) a Posterior network in charge of learning the joint encoded latent distribution of inputs and target data. The initial model, proposed by [3], is optimized by (1) maximizing the overlap of the prior and posterior latent distributions, and (2) minimizing the segmentation loss. The proposed model is designed to be investigated in a simulation environment applied to the real-world application of wildfire segmentation. Specifically, the model is designed to solve the patchy wildfire segmentations of Moderate Resolution Imaging Spectroradiometer (MODIS) by taking the MODIS observations and using Visible Infrared Imaging Radiometer Suite’s (VIIRS) consistent wildfire product as the target. The model solves patchy wildfire segmentations and provides insight into the epistemic errors sourced from model variation. The model utilizes the Born machine as a QUBO solver to represent the latent space as a Bernoulli distribution. The proposed configuration allows the variational segmentation model to leverage the true quantum probabilistic nature and derive a more expressive latent configuration, increasing the model performance in describing wildfire segmentations. The quantum probabilistic information of the Born machine is directly incorporated in the Kullback-Leibler divergence loss in the prior and posterior distributions, forcing the Bernoulli latent distribution to maximize the overlap of input and joint input-target distributions. The proposed model is then trained and compared with a baseline only consisting of direct Bernoulli latent distribution with no Born machine representing the latent space. The models are evaluated based on the segmentation metrics, such as precision, recall, intersect of union, with uncertainty boundaries accounting for the stochastic nature of the model. Our findings show that even in low latent-dimensional space (due to the limit in computational power of the classical quantum simulator), we are able to effectively capture the latent representation and hence the model performs better than the baseline. The findings are a projection for scaling the model into higher dimensional latent space with the Born machine surpassing the baseline performance. Figure 1. Sub-figure (a) demonstrates the architecture for the training phase. The model consists of a Prior and Posterior network that encode inputs and joint input-target data into compact representations, respectively. The Born machine represents the latent distribution, and the U-NET branch learns the segmentation patterns of the data. The stochasticity is introduced to the U-NET through its last layer to create meaningful but stochastic segmentations. Sub-figure (b) represents the inference phase where the model takes the stochastic behavior from the prior network and injects that into the U-NET. Each attempt of inference will generate different but similar segmentations from the same distribution of the wildfire event. REFERENCES [1] Coyle, B., Mills, D., Danos, V., & Kashefi, E. (2020). The Born supremacy: quantum advantage and training of an Ising Born machine. npj Quantum Information, 6(1), 1-11. [2] Liu, J. G., & Wang, L. (2018). Differentiable learning of quantum circuit born machines. Physical Review A, 98(6), 062324. [3] Kohl, S., Romera-Paredes, B., Meyer, C., De Fauw, J., Ledsam, J. R., Maier-Hein, K., ... & Ronneberger, O. (2018). A probabilistic u-net for segmentation of ambiguous images. Advances in neural information processing systems, 31.

quantum machine learning↗

Latent space mapping: Revolutionizing predictive models for divertor plasma detachment control

The inherent complexity of boundary plasma, characterized by multi-scale and multi-physics challenges, has historically restricted high-fidelity simulations to scientific research due to their intensive computational demands. Consequently, routine applications such as discharge control and scenario development have relied on faster but less accurate empirical methods. This work introduces DivControlNN, a novel machine-learning-based surrogate model designed to address these limitations by enabling quasi-real-time predictions (i.e., ~ 0.2 ms) of boundary and divertor plasma behavior. Trained on over 70,000 2D UEDGE simulations from KSTAR tokamak equilibria, DivControlNN employs latent space mapping to efficiently represent complex divertor plasma states, achieving a computational speed-up of over 10 8 compared to traditional simulations while maintaining a relative error below 20% for key plasma property predictions. During the 2024 KSTAR experimental campaign, a prototype detachment control system powered by DivControlNN successfully demonstrated detachment control on its first attempt, even for a new tungsten divertor configuration and without any fine-tuning. These results highlight the transformative potential of DivControlNN in overcoming diagnostic challenges in future fusion reactors by providing fast, robust, and reliable predictions for advanced integrated control systems.

Artificial neural networks↗