微分方程用于多种学科，描述了物理世界的复杂行为。这些方程式的分析解决方案通常很难求解，从而限制了我们目前求解复杂微分方程的能力，并需要将复杂的数值方法近似于解决方案。训练有素的神经网络充当通用函数近似器，能够以新颖的方式求解微分方程。在这项工作中，探索了神经网络算法在数值求解微分方程方面的方法和应用，重点是不同的损失函数和生物应用。传统损失函数和训练参数的变化显示出使神经网络辅助解决方案更有效的希望，从而可以调查更复杂的方程式管理生物学原理。

Many challenging reinforcement learning (RL) problems require designing a distribution of tasks that can be applied to train effective policies. This distribution of tasks can be specified by the curriculum. A curriculum is meant to improve the results of learning and accelerate it. We introduce Success Induced Task Prioritization (SITP), a framework for automatic curriculum learning, where a task sequence is created based on the success rate of each task. In this setting, each task is an algorithmically created environment instance with a unique configuration. The algorithm selects the order of tasks that provide the fastest learning for agents. The probability of selecting any of the tasks for the next stage of learning is determined by evaluating its performance score in previous stages. Experiments were carried out in the Partially Observable Grid Environment for Multiple Agents (POGEMA) and Procgen benchmark. We demonstrate that SITP matches or surpasses the results of other curriculum design methods. Our method can be implemented with handful of minor modifications to any standard RL framework and provides useful prioritization with minimal computational overhead.

The task of video prediction and generation is known to be notoriously difficult, with the research in this area largely limited to short-term predictions. Though plagued with noise and stochasticity, videos consist of features that are organised in a spatiotemporal hierarchy, different features possessing different temporal dynamics. In this paper, we introduce Dynamic Latent Hierarchy (DLH) -- a deep hierarchical latent model that represents videos as a hierarchy of latent states that evolve over separate and fluid timescales. Each latent state is a mixture distribution with two components, representing the immediate past and the predicted future, causing the model to learn transitions only between sufficiently dissimilar states, while clustering temporally persistent states closer together. Using this unique property, DLH naturally discovers the spatiotemporal structure of a dataset and learns disentangled representations across its hierarchy. We hypothesise that this simplifies the task of modeling temporal dynamics of a video, improves the learning of long-term dependencies, and reduces error accumulation. As evidence, we demonstrate that DLH outperforms state-of-the-art benchmarks in video prediction, is able to better represent stochasticity, as well as to dynamically adjust its hierarchical and temporal structure. Our paper shows, among other things, how progress in representation learning can translate into progress in prediction tasks.

Determining and predicting reservoir formation properties for newly drilled wells represents a significant challenge. One of the variations of these properties evaluation is well-interval similarity. Many methodologies for similarity learning exist: from rule-based approaches to deep neural networks. Recently, articles adopted, e.g. recurrent neural networks to build a similarity model as we deal with sequential data. Such an approach suffers from short-term memory, as it pays more attention to the end of a sequence. Neural network with Transformer architecture instead cast their attention over all sequences to make a decision. To make them more efficient in terms of computational time, we introduce a limited attention mechanism similar to Informer and Performer architectures. We conduct experiments on open datasets with more than 20 wells making our experiments reliable and suitable for industrial usage. The best results were obtained with our adaptation of the Informer variant of Transformer with ROC AUC 0.982. It outperforms classical approaches with ROC AUC 0.824, Recurrent neural networks with ROC AUC 0.934 and straightforward usage of Transformers with ROC AUC 0.961.

Recent increases in the computational demands of deep neural networks (DNNs) have sparked interest in efficient deep learning mechanisms, e.g., quantization or pruning. These mechanisms enable the construction of a small, efficient version of commercial-scale models with comparable accuracy, accelerating their deployment to resource-constrained devices. In this paper, we study the security considerations of publishing on-device variants of large-scale models. We first show that an adversary can exploit on-device models to make attacking the large models easier. In evaluations across 19 DNNs, by exploiting the published on-device models as a transfer prior, the adversarial vulnerability of the original commercial-scale models increases by up to 100x. We then show that the vulnerability increases as the similarity between a full-scale and its efficient model increase. Based on the insights, we propose a defense, $similarity$-$unpairing$, that fine-tunes on-device models with the objective of reducing the similarity. We evaluated our defense on all the 19 DNNs and found that it reduces the transferability up to 90% and the number of queries required by a factor of 10-100x. Our results suggest that further research is needed on the security (or even privacy) threats caused by publishing those efficient siblings.

The most widely studied explainable AI (XAI) approaches are unsound. This is the case with well-known model-agnostic explanation approaches, and it is also the case with approaches based on saliency maps. One solution is to consider intrinsic interpretability, which does not exhibit the drawback of unsoundness. Unfortunately, intrinsic interpretability can display unwieldy explanation redundancy. Formal explainability represents the alternative to these non-rigorous approaches, with one example being PI-explanations. Unfortunately, PI-explanations also exhibit important drawbacks, the most visible of which is arguably their size. Recently, it has been observed that the (absolute) rigor of PI-explanations can be traded off for a smaller explanation size, by computing the so-called relevant sets. Given some positive {\delta}, a set S of features is {\delta}-relevant if, when the features in S are fixed, the probability of getting the target class exceeds {\delta}. However, even for very simple classifiers, the complexity of computing relevant sets of features is prohibitive, with the decision problem being NPPP-complete for circuit-based classifiers. In contrast with earlier negative results, this paper investigates practical approaches for computing relevant sets for a number of widely used classifiers that include Decision Trees (DTs), Naive Bayes Classifiers (NBCs), and several families of classifiers obtained from propositional languages. Moreover, the paper shows that, in practice, and for these families of classifiers, relevant sets are easy to compute. Furthermore, the experiments confirm that succinct sets of relevant features can be obtained for the families of classifiers considered.

In this article, the analysis of existing models of satellite image recognition was carried out, the problems in the field of satellite image recognition as a source of information were considered and analyzed, deep learning methods were compared, and existing image recognition methods were analyzed. The results obtained will be used as a basis for the prospective development of a fire recognition model based on satellite images and the use of recognition results as input data for a cognitive model of forecasting the macro-economic situation based on fuzzy cognitive maps.

This paper discusses the development of a convolutional architecture of a deep neural network for the recognition of wildfires on satellite images. Based on the results of image classification, a fuzzy cognitive map of the analysis of the macroeconomic situation was built. The paper also considers the prospect of using hybrid cognitive models for forecasting macroeconomic indicators based on fuzzy cognitive maps using data on recognized wildfires on satellite images.

Quantum machine learning has become an area of growing interest but has certain theoretical and hardware-specific limitations. Notably, the problem of vanishing gradients, or barren plateaus, renders the training impossible for circuits with high qubit counts, imposing a limit on the number of qubits that data scientists can use for solving problems. Independently, angle-embedded supervised quantum neural networks were shown to produce truncated Fourier series with a degree directly dependent on two factors: the depth of the encoding, and the number of parallel qubits the encoding is applied to. The degree of the Fourier series limits the model expressivity. This work introduces two new architectures whose Fourier degrees grow exponentially: the sequential and parallel exponential quantum machine learning architectures. This is done by efficiently using the available Hilbert space when encoding, increasing the expressivity of the quantum encoding. Therefore, the exponential growth allows staying at the low-qubit limit to create highly expressive circuits avoiding barren plateaus. Practically, parallel exponential architecture was shown to outperform the existing linear architectures by reducing their final mean square error value by up to 44.7% in a one-dimensional test problem. Furthermore, the feasibility of this technique was also shown on a trapped ion quantum processing unit.

Powerful hardware services and software libraries are vital tools for quickly and affordably designing, testing, and executing quantum algorithms. A robust large-scale study of how the performance of these platforms scales with the number of qubits is key to providing quantum solutions to challenging industry problems. Such an evaluation is difficult owing to the availability and price of physical quantum processing units. This work benchmarks the runtime and accuracy for a representative sample of specialized high-performance simulated and physical quantum processing units. Results show the QMware cloud computing service can reduce the runtime for executing a quantum circuit by up to 78% compared to the next fastest option for algorithms with fewer than 27 qubits. The AWS SV1 simulator offers a runtime advantage for larger circuits, up to the maximum 34 qubits available with SV1. Beyond this limit, QMware provides the ability to execute circuits as large as 40 qubits. Physical quantum devices, such as Rigetti's Aspen-M2, can provide an exponential runtime advantage for circuits with more than 30. However, the high financial cost of physical quantum processing units presents a serious barrier to practical use. Moreover, of the four quantum devices tested, only IonQ's Harmony achieves high fidelity with more than four qubits. This study paves the way to understanding the optimal combination of available software and hardware for executing practical quantum algorithms.