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.
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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.
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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.
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.
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.
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/.
Parag Jyoti Dutta and Xavier Emery 2024 Mach. Learn.: Sci. Technol. 5 025013
Rock type classification is crucial for evaluating mineral resources in ore deposits and for rock mechanics. Mineral deposits are formed in a variety of rock bodies and rock types. However, the rock type identification in drill core samples is often complicated by overprinting and weathering processes. An approach to classifying rock types from drill core data relies on whole-rock geochemical assays as features. There are few studies on rock type classification from a limited number of metal grades and dry bulk density as features. The novelty in our approach is the introduction of two sets of feature variables (proxies) at sampled data points, generated by geostatistical leave-one-out cross-validation and by kriging for removing short-scale spatial variation of the measured features. We applied our proposal to a dataset from a porphyry Cu–Au deposit in Mongolia. The model performances on a testing data subset indicate that, when the training dataset is not large, the performance of the classifier (a random forest) substantially improves by incorporating the proxy features as a complement to the original measured features. At each training data point, these proxy features throw light based on the underlying spatial data correlation structure, scales of variations, sampling design, and values of features observed at neighboring points, and show the benefits of combining geostatistics with machine learning.
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.
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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.
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.
Leonardo Banchi 2024 Mach. Learn.: Sci. Technol. 5 025036
Many inference scenarios rely on extracting relevant information from known data in order to make future predictions. When the underlying stochastic process satisfies certain assumptions, there is a direct mapping between its exact classical and quantum simulators, with the latter asymptotically using less memory. Here we focus on studying whether such quantum advantage persists when those assumptions are not satisfied, and the model is doomed to have imperfect accuracy. By studying the trade-off between accuracy and memory requirements, we show that quantum models can reach the same accuracy with less memory, or alternatively, better accuracy with the same memory. Finally, we discuss the implications of this result for learning tasks.
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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.
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Heinen et al
For many machine learning applications in science, data acquisition, not training, is the bottleneck even when avoiding experiments and relying on computation and simulation. 
Correspondingly, and in order to reduce cost and carbon footprint, training data efficiency is key. 
We introduce minimal multilevel machine learning (M3L) which 
optimizes training data set sizes using a loss function at multiple levels of reference data in order to minimize a combination of prediction error with overall training data acquisition costs (as measured by computational wall-times).
Numerical evidence has been obtained for calculated atomization energies and electron affinities of thousands of organic molecules at various levels of theory including HF, MP2, DLPNO-CCSD(T), DFHFCABS, PNOMP2F12, and PNOCCSD(T)F12, and treating them with 
basis sets TZ, cc-pVTZ, and AVTZ-F12.
Our M3L benchmarks for reaching chemical accuracy in distinct chemical compound sub-spaces 
indicate substantial computational cost reductions by factors of 
$\sim$ 1.01, 1.1, 3.8, 13.8, and 25.8 when compared to heuristic sub-optimal multilevel machine learning (M2L) for the data sets QM7b, QM9$^\mathrm{LCCSD(T)}$, EGP, QM9$^\mathrm{CCSD(T)}_\mathrm{AE}$, and QM9$^\mathrm{CCSD(T)}_\mathrm{EA}$, respectively.
Furthermore, we use M2L to investigate the performance for 76 density functionals when used within multilevel learning and building on the following levels drawn from the hierarchy of Jacobs Ladder:~LDA, GGA, mGGA, and hybrid functionals.
Within M2L and the molecules considered, 
mGGAs do not provide any noticeable advantage over GGAs. 
Among the functionals considered and in combination with LDA, the three on average top performing GGA and Hybrid levels for atomization energies on QM9 using M3L correspond respectively to PW91, KT2, B97D, and $\tau$-HCTH, B3LYP$\ast$(VWN5), and TPSSH.
Li et al
Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard approach to such problems, with one of the most successful methods employing tensor products between various tensors that transform under the spatial group. However, as the number of different tensors and the complexity of relationships between them increase, maintaining parsimony and equivariance becomes increasingly challenging. In this paper, we propose using fusion diagrams, a technique widely employed in simulating SU($2$)-symmetric quantum many-body problems, to design new equivariant components for equivariant neural networks. This results in a diagrammatic approach to constructing novel neural network architectures. When applied to particles within a given local neighborhood, the resulting components, which we term "fusion blocks," serve as universal approximators of any continuous equivariant function defined on the neighborhood. We incorporate a fusion block into pre-existing equivariant architectures (Cormorant and MACE), leading to improved performance with fewer parameters on a range of challenging chemical problems. Furthermore, we apply group-equivariant neural networks to study non-adiabatic molecular dynamics of stilbene cis-trans isomerization and water adsorption cycles in porous materials, such as metal-organic frameworks. Our approach, which combines tensor networks with equivariant neural networks, suggests a potentially fruitful direction for designing more expressive equivariant neural networks.
Fox et al
Symbolic Regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets.
We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order of magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find incorporating these constraints in Bayesian SR (as the Bayesian prior) is better than by modifying the fitness function in the GA.
Messai et al
Meningitis, characterized by meninges and cerebrospinal fluid (CSF) inflammation, poses diagnostic challenges due to diverse clinical manifestations. This work introduces an explainable AI automatic medical decision methodology that determines critical features and their relevant values for the differential diagnosis of various meningitis cases. We proceed with knowledge acquisition to define the rules for this research. Currently, we have established the etiological diagnosis of Meningococcaemia, Meningococcal Meningitis, Tuberculous Meningitis, Aseptic Meningitis, Haemophilus influenzae Meningitis, and Pneumococcal
Meningitis. The data preprocessing was conducted after collecting data from samples with meningitis diseases at Setif Hospital in Algeria. Tree-based ensemble methods were then applied to assess the model's performance. Finally, we implement an XAI agnostic explainability approach based on the SHapley Additive exPlanations technique to attribute each feature's contribution to the model's output. Experiments were conducted on the collected dataset and the SINAN database, obtained from the Brazilian Government's Health Information System on Notifiable Diseases, which comprises 6729 patients aged over 18 years. The Extreme Gradient Boosting model was chosen for its superior performance metrics (Accuracy: 0.90, AUROC: 0.94, and F1-score: 0.98). Setif's hospital data revealed notable performance metrics (Accuracy: 0.7143, F1-Score: 0.7857). This study's findings showcase each feature's contribution to the model's predictions and diagnosis. It also reveals critical biomarker ranges associated with distinct types of Meningitis. Significant diagnostic effect was found for Meningococcal Meningitis with elevated neutrophil levels (>40%) and balanced lymphocyte levels (40-60%). Tuberculous Meningitis demonstrated low neutrophil levels (<60%) and elevated lymphocyte levels (>60%). Haemophilus influenzae meningitis exhibited a predominance of neutrophils (>80%), while Aseptic meningitis showed lower neutrophil levels (<40%) and lymphocyte levels within the range of 50-60%. The majority of the AI automatic medical decision results are twinned with validation by our team of infectious disease experts, confirming the alignment of algorithmic diagnoses with clinical practices.
Belyshev et al
The discovery of conservation principles is crucial for understanding the fundamental behavior of both classical and quantum physical systems across numerous domains. This paper introduces an innovative method that merges representation learning and topological analysis to explore the topology of conservation law spaces. Notably, the robustness of our approach to noise makes it suitable for complex experimental setups and its aptitude extends to the analysis of quantum systems, as successfully demonstrated in our paper. We exemplify our method's potential to unearth previously unknown conservation principles and endorse interdisciplinary research through a variety of physical simulations. In conclusion, this work emphasizes the significance of data-driven techniques in deepening our comprehension of the principles governing classical and quantum physical systems.