Transformer models coupled with a simplified molecular line entry system (SMILES) have recently proven to be a powerful combination for solving challenges in cheminformatics. These models, however, are often developed specifically for a single application and can be very resource-intensive to train. In this work we present the Chemformer model—a Transformer-based model which can be quickly applied to both sequence-to-sequence and discriminative cheminformatics tasks. Additionally, we show that self-supervised pre-training can improve performance and significantly speed up convergence on downstream tasks. On direct synthesis and retrosynthesis prediction benchmark datasets we publish state-of-the-art results for top-1 accuracy. We also improve on existing approaches for a molecular optimisation task and show that Chemformer can optimise on multiple discriminative tasks simultaneously. Models, datasets and code will be made available after publication.
Purpose-led Publishing is a coalition of three not-for-profit publishers in the field of physical sciences: AIP Publishing, the American Physical Society and IOP Publishing.
Together, as publishers that will always put purpose above profit, we have defined a set of industry standards that underpin high-quality, ethical scholarly communications.
We are proudly declaring that science is our only shareholder.
ISSN: 2632-2153
Machine Learning: Science and Technology is a multidisciplinary open access journal that bridges the application of machine learning across the sciences with advances in machine learning methods and theory as motivated by physical insights.
Open all abstracts, in this tab
Ross Irwin et al 2022 Mach. Learn.: Sci. Technol. 3 015022
Tanujit Chakraborty et al 2024 Mach. Learn.: Sci. Technol. 5 011001
Generative adversarial networks (GANs) have rapidly emerged as powerful tools for generating realistic and diverse data across various domains, including computer vision and other applied areas, since their inception in 2014. Consisting of a discriminative network and a generative network engaged in a minimax game, GANs have revolutionized the field of generative modeling. In February 2018, GAN secured the leading spot on the 'Top Ten Global Breakthrough Technologies List' issued by the Massachusetts Science and Technology Review. Over the years, numerous advancements have been proposed, leading to a rich array of GAN variants, such as conditional GAN, Wasserstein GAN, cycle-consistent GAN, and StyleGAN, among many others. This survey aims to provide a general overview of GANs, summarizing the latent architecture, validation metrics, and application areas of the most widely recognized variants. We also delve into recent theoretical developments, exploring the profound connection between the adversarial principle underlying GAN and Jensen–Shannon divergence while discussing the optimality characteristics of the GAN framework. The efficiency of GAN variants and their model architectures will be evaluated along with training obstacles as well as training solutions. In addition, a detailed discussion will be provided, examining the integration of GANs with newly developed deep learning frameworks such as transformers, physics-informed neural networks, large language models, and diffusion models. Finally, we reveal several issues as well as future research outlines in this field.
Ivan S Novikov et al 2021 Mach. Learn.: Sci. Technol. 2 025002
The subject of this paper is the technology (the 'how') of constructing machine-learning interatomic potentials, rather than science (the 'what' and 'why') of atomistic simulations using machine-learning potentials. Namely, we illustrate how to construct moment tensor potentials using active learning as implemented in the MLIP package, focusing on the efficient ways to automatically sample configurations for the training set, how expanding the training set changes the error of predictions, how to set up ab initio calculations in a cost-effective manner, etc. The MLIP package (short for Machine-Learning Interatomic Potentials) is available at https://mlip.skoltech.ru/download/.
Philippe Schwaller et al 2021 Mach. Learn.: Sci. Technol. 2 015016
Artificial intelligence is driving one of the most important revolutions in organic chemistry. Multiple platforms, including tools for reaction prediction and synthesis planning based on machine learning, have successfully become part of the organic chemists' daily laboratory, assisting in domain-specific synthetic problems. Unlike reaction prediction and retrosynthetic models, the prediction of reaction yields has received less attention in spite of the enormous potential of accurately predicting reaction conversion rates. Reaction yields models, describing the percentage of the reactants converted to the desired products, could guide chemists and help them select high-yielding reactions and score synthesis routes, reducing the number of attempts. So far, yield predictions have been predominantly performed for high-throughput experiments using a categorical (one-hot) encoding of reactants, concatenated molecular fingerprints, or computed chemical descriptors. Here, we extend the application of natural language processing architectures to predict reaction properties given a text-based representation of the reaction, using an encoder transformer model combined with a regression layer. We demonstrate outstanding prediction performance on two high-throughput experiment reactions sets. An analysis of the yields reported in the open-source USPTO data set shows that their distribution differs depending on the mass scale, limiting the data set applicability in reaction yields predictions.
Mario Krenn et al 2020 Mach. Learn.: Sci. Technol. 1 045024
The discovery of novel materials and functional molecules can help to solve some of society's most urgent challenges, ranging from efficient energy harvesting and storage to uncovering novel pharmaceutical drug candidates. Traditionally matter engineering–generally denoted as inverse design–was based massively on human intuition and high-throughput virtual screening. The last few years have seen the emergence of significant interest in computer-inspired designs based on evolutionary or deep learning methods. The major challenge here is that the standard strings molecular representation SMILES shows substantial weaknesses in that task because large fractions of strings do not correspond to valid molecules. Here, we solve this problem at a fundamental level and introduce SELFIES (SELF-referencIng Embedded Strings), a string-based representation of molecules which is 100% robust. Every SELFIES string corresponds to a valid molecule, and SELFIES can represent every molecule. SELFIES can be directly applied in arbitrary machine learning models without the adaptation of the models; each of the generated molecule candidates is valid. In our experiments, the model's internal memory stores two orders of magnitude more diverse molecules than a similar test with SMILES. Furthermore, as all molecules are valid, it allows for explanation and interpretation of the internal working of the generative models.
Steven Dahdah and James Richard Forbes 2024 Mach. Learn.: Sci. Technol. 5 025038
This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an infinite set of lifting functions. A finite-dimensional approximation of the Koopman operator can be identified from data by choosing a finite subset of lifting functions and solving a regression problem in the lifted space. Existing methods are designed to identify open-loop systems. However, it is impractical or impossible to run experiments on some systems, such as unstable systems, in an open-loop fashion. The proposed method leverages the linearity of the Koopman operator, along with knowledge of the controller and the structure of the closed-loop (CL) system, to simultaneously identify the CL and plant systems. The advantages of the proposed CL Koopman operator approximation method are demonstrated in simulation using a Duffing oscillator and experimentally using a rotary inverted pendulum system. An open-source software implementation of the proposed method is publicly available, along with the experimental dataset generated for this paper.
Moritz Hoffmann et al 2022 Mach. Learn.: Sci. Technol. 3 015009
Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software. Deeptime can be found under https://deeptime-ml.github.io/.
Pablo Lemos et al 2023 Mach. Learn.: Sci. Technol. 4 045002
We present an approach for using machine learning to automatically discover the governing equations and unknown properties (in this case, masses) of real physical systems from observations. We train a 'graph neural network' to simulate the dynamics of our Solar System's Sun, planets, and large moons from 30 years of trajectory data. We then use symbolic regression to correctly infer an analytical expression for the force law implicitly learned by the neural network, which our results showed is equivalent to Newton's law of gravitation. The key assumptions our method makes are translational and rotational equivariance, and Newton's second and third laws of motion. It did not, however, require any assumptions about the masses of planets and moons or physical constants, but nonetheless, they, too, were accurately inferred with our method. Naturally, the classical law of gravitation has been known since Isaac Newton, but our results demonstrate that our method can discover unknown laws and hidden properties from observed data.
Jeffrey M Ede 2021 Mach. Learn.: Sci. Technol. 2 011004
Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy.
Arsenii Senokosov et al 2024 Mach. Learn.: Sci. Technol. 5 015040
Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.
Open all abstracts, in this tab
Amanda Howard et al 2024 Mach. Learn.: Sci. Technol. 5 025042
We introduce a novel continual learning method based on multifidelity deep neural networks. This method learns the correlation between the output of previously trained models and the desired output of the model on the current training dataset, limiting catastrophic forgetting. On its own the multifidelity continual learning method shows robust results that limit forgetting across several datasets. Additionally, we show that the multifidelity method can be combined with existing continual learning methods, including replay and memory aware synapses, to further limit catastrophic forgetting. The proposed continual learning method is especially suited for physical problems where the data satisfy the same physical laws on each domain, or for physics-informed neural networks, because in these cases we expect there to be a strong correlation between the output of the previous model and the model on the current training domain.
Hussain Ahmad Madni et al 2024 Mach. Learn.: Sci. Technol. 5 025041
Federated learning (FL) is an evolving machine learning technique that allows collaborative model training without sharing the original data among participants. In real-world scenarios, data residing at multiple clients are often heterogeneous in terms of different resolutions, magnifications, scanners, or imaging protocols, and thus challenging for global FL model convergence in collaborative training. Most of the existing FL methods consider data heterogeneity within one domain by assuming same data variation in each client site. In this paper, we consider data heterogeneity in FL with different domains of heterogeneous data by raising the problems of domain-shift, class-imbalance, and missing data. We propose a method, multi-domain FL as a solution to heterogeneous training data from multiple domains by training robust vision transformer model. We use two loss functions, one for correctly predicting class labels and other for encouraging similarity and dissimilarity over latent features, to optimize the global FL model. We perform various experiments using different convolution-based networks and non-convolutional Transformer architectures on multi-domain datasets. We evaluate the proposed approach on benchmark datasets and compare with the existing FL methods. Our results show the superiority of the proposed approach which performs better in term of robust FL global model than the exiting methods.
Shahin Alipour Bonab et al 2024 Mach. Learn.: Sci. Technol. 5 025040
Index-value, or so-called n-value prediction is of paramount importance for understanding the superconductors' behaviour specially when modeling of superconductors is needed. This parameter is dependent on several physical quantities including temperature, the magnetic field's density and orientation, and affects the behaviour of high-temperature superconducting devices made out of coated conductors in terms of losses and quench propagation. In this paper, a comprehensive analysis of many machine learning (ML) methods for estimating the n-value has been carried out. The results demonstrated that cascade forward neural network (CFNN) excels in this scope. Despite needing considerably higher training time when compared to the other attempted models, it performs at the highest accuracy, with 0.48 root mean squared error (RMSE) and 99.72% Pearson coefficient for goodness of fit (R-squared). In contrast, the rigid regression method had the worst predictions with 4.92 RMSE and 37.29% R-squared. Also, random forest, boosting methods, and simple feed forward neural network can be considered as a middle accuracy model with faster training time than CFNN. The findings of this study not only advance modeling of superconductors but also pave the way for applications and further research on ML plug-and-play codes for superconducting studies including modeling of superconducting devices.
Cafer Tufan Cakir et al 2024 Mach. Learn.: Sci. Technol. 5 025037
In materials science, traditional techniques for analyzing layered structures are essential for obtaining information about local structure, electronic properties and chemical states. While valuable, these methods often require high vacuum environments and have limited depth profiling capabilities. The grazing exit x-ray absorption near-edge structure (GE-XANES) technique addresses these limitations by providing depth-resolved insight at ambient conditions, facilitating in situ material analysis without special sample preparation. However, GE-XANES is limited by long data acquisition times, which hinders its practicality for various applications. To overcome this, we have incorporated Bayesian optimization (BO) into the GE-XANES data acquisition process. This innovative approach potentially reduces measurement time by a factor of 50. We have used a standard GE-XANES experiment, which serve as reference, to validate the effectiveness and accuracy of the BO-informed experimental setup. Our results show that this optimized approach maintains data quality while significantly improving efficiency, making GE-XANES more accessible to a wider range of materials science applications.
Javier E Santos et al 2024 Mach. Learn.: Sci. Technol. 5 025039
Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics—in particular, confinement effects which vary across the nanoscale to the microscale. While numerical simulation is possible, the computational cost is prohibitive for realistic domains, which are large and complex. Although machine learning (ML) models have been proposed to circumvent simulation, none so far has simultaneously accounted for heterogeneous 3D structures, fluid confinement effects, and multiple simulation resolutions. By utilizing numerous computer science techniques to improve the scalability of training, we have for the first time developed a general flow model that accounts for the pore-structure and corresponding physical phenomena at scales from Angstrom to the micrometer. Using synthetic computational domains for training, our ML model exhibits strong performance (R2 = 0.9) when tested on extremely diverse real domains at multiple scales.
Open all abstracts, in this tab
Tanujit Chakraborty et al 2024 Mach. Learn.: Sci. Technol. 5 011001
Generative adversarial networks (GANs) have rapidly emerged as powerful tools for generating realistic and diverse data across various domains, including computer vision and other applied areas, since their inception in 2014. Consisting of a discriminative network and a generative network engaged in a minimax game, GANs have revolutionized the field of generative modeling. In February 2018, GAN secured the leading spot on the 'Top Ten Global Breakthrough Technologies List' issued by the Massachusetts Science and Technology Review. Over the years, numerous advancements have been proposed, leading to a rich array of GAN variants, such as conditional GAN, Wasserstein GAN, cycle-consistent GAN, and StyleGAN, among many others. This survey aims to provide a general overview of GANs, summarizing the latent architecture, validation metrics, and application areas of the most widely recognized variants. We also delve into recent theoretical developments, exploring the profound connection between the adversarial principle underlying GAN and Jensen–Shannon divergence while discussing the optimality characteristics of the GAN framework. The efficiency of GAN variants and their model architectures will be evaluated along with training obstacles as well as training solutions. In addition, a detailed discussion will be provided, examining the integration of GANs with newly developed deep learning frameworks such as transformers, physics-informed neural networks, large language models, and diffusion models. Finally, we reveal several issues as well as future research outlines in this field.
Jakub Rydzewski et al 2023 Mach. Learn.: Sci. Technol. 4 031001
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex systems where even thousands of degrees of freedom are sampled. An abundance of such data makes gaining insight into a specific physical problem strenuous. Our primary aim in this review is to focus on unsupervised machine learning methods that can be used on simulation data to find a low-dimensional manifold providing a collective and informative characterization of the studied process. Such manifolds can be used for sampling long-timescale processes and free-energy estimation. We describe methods that can work on datasets from standard and enhanced sampling atomistic simulations. Unlike recent reviews on manifold learning for atomistic simulations, we consider only methods that construct low-dimensional manifolds based on Markov transition probabilities between high-dimensional samples. We discuss these techniques from a conceptual point of view, including their underlying theoretical frameworks and possible limitations.
James Stokes et al 2023 Mach. Learn.: Sci. Technol. 4 021001
This article aims to summarize recent and ongoing efforts to simulate continuous-variable quantum systems using flow-based variational quantum Monte Carlo techniques, focusing for pedagogical purposes on the example of bosons in the field amplitude (quadrature) basis. Particular emphasis is placed on the variational real- and imaginary-time evolution problems, carefully reviewing the stochastic estimation of the time-dependent variational principles and their relationship with information geometry. Some practical instructions are provided to guide the implementation of a PyTorch code. The review is intended to be accessible to researchers interested in machine learning and quantum information science.
Bahram Jalali et al 2022 Mach. Learn.: Sci. Technol. 3 041001
The phenomenal success of physics in explaining nature and engineering machines is predicated on low dimensional deterministic models that accurately describe a wide range of natural phenomena. Physics provides computational rules that govern physical systems and the interactions of the constituents therein. Led by deep neural networks, artificial intelligence (AI) has introduced an alternate data-driven computational framework, with astonishing performance in domains that do not lend themselves to deterministic models such as image classification and speech recognition. These gains, however, come at the expense of predictions that are inconsistent with the physical world as well as computational complexity, with the latter placing AI on a collision course with the expected end of the semiconductor scaling known as Moore's Law. This paper argues how an emerging symbiosis of physics and AI can overcome such formidable challenges, thereby not only extending AI's spectacular rise but also transforming the direction of engineering and physical science.
April M Miksch et al 2021 Mach. Learn.: Sci. Technol. 2 031001
Recent advances in machine-learning interatomic potentials have enabled the efficient modeling of complex atomistic systems with an accuracy that is comparable to that of conventional quantum-mechanics based methods. At the same time, the construction of new machine-learning potentials can seem a daunting task, as it involves data-science techniques that are not yet common in chemistry and materials science. Here, we provide a tutorial-style overview of strategies and best practices for the construction of artificial neural network (ANN) potentials. We illustrate the most important aspects of (a) data collection, (b) model selection, (c) training and validation, and (d) testing and refinement of ANN potentials on the basis of practical examples. Current research in the areas of active learning and delta learning are also discussed in the context of ANN potentials. This tutorial review aims at equipping computational chemists and materials scientists with the required background knowledge for ANN potential construction and application, with the intention to accelerate the adoption of the method, so that it can facilitate exciting research that would otherwise be challenging with conventional strategies.
Open all abstracts, in this tab
Tian et al
We present a new class of AI models for 
the detection of quasi-circular, spinning, 
non-precessing binary black hole mergers 
whose waveforms include the higher order gravitational wave modes $(\ell, |m|)=\{(2, 2), (2, 1), (3, 3), 
(3, 2), (4, 4)\}$, and mode mixing effects 
in the \(\ell = 3, |m| = 2\) harmonics. 
These AI models combine hybrid dilated convolution 
neural networks to accurately model both short- and long-range 
temporal sequential information of gravitational waves; 
and graph neural networks to capture spatial 
correlations among gravitational wave observatories 
to consistently describe and identify the presence of a signal 
in a three detector network encompassing the Advanced 
LIGO and Virgo detectors. We first trained these 
spatiotemporal-graph AI models using synthetic noise, 
using 1.2 million modeled waveforms to densely sample this 
signal manifold, within 1.7 hours using 256 NVIDIA 
A100 GPUs in the Polaris 
supercomputer at the Argonne Leadership Computing 
Facility. This distributed training approach exhibited optimal classification performance, and strong 
scaling up to 512 NVIDIA 
A100 GPUs. With these AI 
ensembles we processed data from a three detector 
network, and found that an 
ensemble of 4 AI models achieves 
state-of-the-art 
performance for signal detection, and reports two 
misclassifications for every decade of 
searched data. We distributed AI inference over 
128 GPUs in the Polaris 
supercomputer and 128 nodes in the Theta supercomputer, 
and completed the processing of a decade of gravitational 
wave data from a three detector network within 3.5 hours. 
Finally, we fine-tuned 
these AI ensembles to 
process the entire month of February 2020, 
which is part of the O3b 
LIGO/Virgo observation run, and found 6 gravitational waves, 
concurrently identified in Advanced LIGO and 
Advanced Virgo data, and zero false positives. 
This analysis was completed in one hour using one 
NVIDIA A100 GPU.
Lyu et al
Precise liver tumors and associated organ segmentation hold immense value for surgical and radiological intervention, enabling anatomical localization for pre-operative planning and intra-operative guidance. Modern deep learning models for medical image segmentation have evolved from convolution neural networks to transformer architectures, significantly boosting global context understanding. However, accurate delineation especially of hepatic lesions remains an enduring challenge due to models' predominant focus solely on spatial feature extraction failing to adequately characterize complex medical anatomies. Moreover, the relative paucity of expertly annotated medical imaging data restricts model exposure to diverse pathological presentations. In this paper, we present a three-phrased cascaded segmentation framework featuring an X-Fuse model that synergistically integrates spatial and frequency domain's complementary information in dual encoders to enrich latent feature representation. To enhance model generalizability, building upon X Fuse topology and taking advantage of additional unlabeled pathological data, our proposed integration of curriculum pseudo-labeling with Jensen-Shannon variance-based uncertainty rectification promotes optimized pseudo-supervision in the context of semi-supervised learning. We further introduce a tumor-focus augmentation technique including training-free copy-paste and knowledge-based synthesis that show efficacy in simplicity, contributing to the substantial elevation of model adaptability on diverse lesional morphologies. Extensive experiments and modular evaluations on a holdout test set demonstrate that our methods significantly outperform existing state-of-the-art segmentation models in both supervised and semi-supervised settings, as measured by the Dice similarity coefficient, achieving superior delineation of bones (95.42%), liver (96.26%), and liver tumors (89.53%) with 16.41% increase comparing to V-Net on supervised-only and augmented-absent scenario. Our method marks a significant step toward the realization of more reliable and robust AI-assisted diagnostic tools for liver tumor intervention. We have made the codes publicly available.
Ibebuchi et al
The temporal resolution of environmental data sets plays a major role in the granularity of the information that can be derived from the data. In most cases, it is required that different data sets have a common temporal resolution to enable their consistent evaluations and applications in making informed decisions. This study leverages deep learning with long short-term memory (LSTM) neural networks and model inference to enhance the temporal resolution of climate datasets, specifically temperature, and precipitation, from daily to sub-daily scales. We trained our model to learn the relationship between daily and sub-daily data, subsequently applying this knowledge to increase the resolution of a separate dataset with a coarser (daily) temporal resolution. Our findings reveal a high degree of accuracy for temperature predictions, evidenced by a correlation of 0.99 and a mean absolute error of 0.21 °C, between the actual and predicted sub-daily values. In contrast, the approach was less effective for precipitation, achieving an explained variance of only 37%, compared to 98% for temperature. Further, besides the sub-daily interpolation of the climate data sets, we adapted our approach to increase the resolution of the Normalized difference vegetation index of Landsat (from 16-day to 5-day interval) using the LSTM model pre-trained from the Sentinel 2 Normalized difference vegetation index - that exists at a relatively higher temporal resolution. The explained variance between the predicted Landsat and Sentinel 1 data is 70% with a mean absolute error of 0.03. These results suggest that our method is particularly suitable for environmental datasets with less pronounced short-term variability, offering a promising tool for improving the resolution and utility of the data.
Zeng et al
While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization with internal linear layers and $L_2$ regularization (weight decay) to automatically estimate the underlying dimensionality of a data set, produce an orthogonal manifold coordinate system, and provide the mapping functions between the ambient space and manifold space, allowing for out-of-sample projections. We validate our framework's ability to estimate the manifold dimension for a series of datasets from dynamical systems of varying complexities and compare to other state-of-the-art estimators. We analyze the training dynamics of the network to glean insight into the mechanism of low-rank learning and find that collectively each of the implicit regularizing layers compound the low-rank representation and even self-correct during training. Analysis of gradient descent dynamics for this architecture in the linear case reveals the role of the internal linear layers in leading to faster decay of a ``collective weight variable" incorporating all layers, and the role of weight decay in breaking degeneracies and thus driving convergence along directions in which no decay would occur in its absence. We show that this framework can be naturally extended for applications of state-space modeling and forecasting by generating a data-driven dynamic model of a spatiotemporally chaotic partial differential equation using only the manifold coordinates. Finally, we demonstrate that our framework is robust to hyperparameter choices.
Carvalho et al
We explore the possibility of fully replacing a plasma physics kinetic simulator with a graph neural network-based simulator. We focus on this class of surrogate models given the similarity between their message-passing update mechanism and the traditional physics solver update, and the possibility of enforcing known physical priors into the graph construction and update. We show that our model learns the kinetic plasma dynamics of the one-dimensional plasma model, a predecessor of contemporary kinetic plasma simulation codes, and recovers a wide range of well-known kinetic plasma processes, including plasma thermalization, electrostatic fluctuations about thermal equilibrium, and the drag on a fast sheet and Landau damping. We compare the performance against the original plasma model in terms of run-time, conservation laws, and temporal evolution of key physical quantities. The limitations of the model are presented and possible directions for higher-dimensional surrogate models for kinetic plasmas are discussed.