The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research.

Satellite data of atmospheric pollutants are often available only at coarse spatial resolution, limiting their applicability in local-scale environmental analysis and decision-making. Spatial downscaling methods aim to transform the coarse satellite data into high-resolution fields. In this work, two widely used deep learning architectures, the super-resolution deep residual network (SRDRN) and the encoder-decoder-based UNet, are considered for spatial downscaling of tropospheric ozone. Both methods are extended with a lightweight temporal module, which encodes observation time using either sinusoidal or radial basis function (RBF) encoding, and fuses the temporal features with the spatial representations in the networks. The proposed time-aware extensions are evaluated against their baseline counterparts in a case study on ozone downscaling over Italy. The results suggest that, while only slightly increasing computational complexity, the temporal modules significantly improve downscaling performance and convergence speed.

Accurate and compact representation of signed distance functions (SDFs) of implicit surfaces is crucial for efficient storage, computation, and downstream processing of 3D geometry. In this work, we propose a general learning method for approximating precomputed SDF fields of implicit surfaces by a relatively small number of ellipsoidal radial basis functions (ERBFs). The SDF values could be computed from various sources, including point clouds, triangle meshes, analytical expressions, pretrained neural networks, etc. Given SDF values on spatial grid points, our method approximates the SDF using as few ERBFs as possible, achieving a compact representation while preserving the geometric shape of the corresponding implicit surface. To balance sparsity and approximation precision, we introduce a dynamic multi-objective optimization strategy, which adaptively incorporates regularization to enforce sparsity and jointly optimizes the weights, centers, shapes, and orientations of the ERBFs. For computational efficiency, a nearest-neighbor-based data structure restricts computations to points near each kernel center, and CUDA-based parallelism further accelerates the optimization. Furthermore, a hierarchical refinement strategy based on SDF spatial grid points progressively incorporates coarse-to-fine samples for parameter initialization and optimization, improving convergence and training efficiency. Extensive experiments on multiple benchmark datasets demonstrate that our method can represent SDF fields with significantly fewer parameters than existing sparse implicit representation approaches, achieving better accuracy, robustness, and computational efficiency. The corresponding executable program is publicly available at https://github.com/lianbobo/SE-RBFNet.git

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research.

Deep learning has gained attention for solving PDEs, but the black-box nature of neural networks hinders precise enforcement of boundary conditions. To address this, we propose a boundary condition-guaranteed evolutionary Kolmogorov-Arnold Network (KAN) with radial basis functions (BEKAN). In BEKAN, we propose three distinct and combinable approaches for incorporating Dirichlet, periodic, and Neumann boundary conditions into the network. For Dirichlet problem, we use smooth and global Gaussian RBFs to construct univariate basis functions for approximating the solution and to encode boundary information at the activation level of the network. To handle periodic problems, we employ a periodic layer constructed from a set of sinusoidal functions to enforce the boundary conditions exactly. For a Neumann problem, we devise a least-squares formulation to guide the parameter evolution toward satisfying the Neumann condition. By virtue of the boundary-embedded RBFs, the periodic layer, and the evolutionary framework, we can perform accurate PDE simulations while rigorously enforcing boundary conditions. For demonstration, we conducted extensive numerical experiments on Dirichlet, Neumann, periodic, and mixed boundary value problems. The results indicate that BEKAN outperforms both multilayer perceptron (MLP) and B-splines KAN in terms of accuracy. In conclusion, the proposed approach enhances the capability of KANs in solving PDE problems while satisfying boundary conditions, thereby facilitating advancements in scientific computing and engineering applications.

In this article, we introduce a novel deep learning hybrid model that integrates attention Transformer and Gated Recurrent Unit (GRU) architectures to improve the accuracy of cryptocurrency price predictions. By combining the Transformer's strength in capturing long-range patterns with the GRU's ability to model short-term and sequential trends, the hybrid model provides a well-rounded approach to time series forecasting. We apply the model to predict the daily closing prices of Bitcoin and Ethereum based on historical data that include past prices, trading volumes, and the Fear and Greed index. We evaluate the performance of our proposed model by comparing it with four other machine learning models: two are non-sequential feedforward models: Radial Basis Function Network (RBFN) and General Regression Neural Network (GRNN), and two are bidirectional sequential memory-based models: Bidirectional Long-Short-Term Memory (BiLSTM) and Bidirectional Gated Recurrent Unit (BiGRU). The performance of the model is assessed using several metrics, including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE), along with statistical validation through the nonparametric Friedman test followed by a post hoc Wilcoxon signed rank test. The results demonstrate that our hybrid model consistently achieves superior accuracy, highlighting its effectiveness for financial prediction tasks. These findings provide valuable insights for improving real-time decision making in cryptocurrency markets and support the growing use of hybrid deep learning models in financial analytics.

This paper presents the Visual Place Cell Encoding (VPCE) model, a biologically inspired computational framework for simulating place cell-like activation using visual input. Drawing on evidence that visual landmarks play a central role in spatial encoding, the proposed VPCE model activates visual place cells by clustering high-dimensional appearance features extracted from images captured by a robot-mounted camera. Each cluster center defines a receptive field, and activation is computed based on visual similarity using a radial basis function. We evaluate whether the resulting activation patterns correlate with key properties of biological place cells, including spatial proximity, orientation alignment, and boundary differentiation. Experiments demonstrate that the VPCE can distinguish between visually similar yet spatially distinct locations and adapt to environment changes such as the insertion or removal of walls. These results suggest that structured visual input, even in the absence of motion cues or reward-driven learning, is sufficient to generate place-cell-like spatial representations and support biologically inspired cognitive mapping.

Crystal structure forms the foundation for understanding the physical and chemical properties of materials. Generative models have emerged as a new paradigm in crystal structure prediction(CSP), however, accurately capturing key characteristics of crystal structures, such as periodicity and symmetry, remains a significant challenge. In this paper, we propose a Transformer-Enhanced Variational Autoencoder for Crystal Structure Prediction (TransVAE-CSP), who learns the characteristic distribution space of stable materials, enabling both the reconstruction and generation of crystal structures. TransVAE-CSP integrates adaptive distance expansion with irreducible representation to effectively capture the periodicity and symmetry of crystal structures, and the encoder is a transformer network based on an equivariant dot product attention mechanism. Experimental results on the carbon_24, perov_5, and mp_20 datasets demonstrate that TransVAE-CSP outperforms existing methods in structure reconstruction and generation tasks under various modeling metrics, offering a powerful tool for crystal structure design and optimization.

High-fidelity speech enhancement often requires sophisticated modeling to capture intricate, multiscale patterns. Standard activation functions, while introducing nonlinearity, lack the flexibility to fully address this complexity. Kolmogorov-Arnold Networks (KAN), an emerging methodology that employs learnable activation functions on graph edges, present a promising alternative. This work investigates two novel KAN variants based on rational and radial basis functions for speech enhancement. We integrate the rational variant into the 1D CNN blocks of Demucs and the GRU-Transformer blocks of MP-SENet, while the radial variant is adapted to the 2D CNN-based decoders of MP-SENet. Experiments on the VoiceBank-DEMAND dataset show that replacing standard activations with KAN-based activations improves speech quality across both the time-domain and time-frequency domain methods with minimal impact on model size and FLOP, underscoring KAN's potential to improve speech enhancement models.

Scientific computing has benefited from using operator networks to enhance or replace numerical computation for the purpose of simulation and forecasting on a wide array of applications to include computational fluid dynamics and weather forecasting [3]. The two primary neural operators that demonstrated immediate success are the deep operator network (DeepONet) [4] based on the universal approximation theorem in [5], and the Fourier neural operator (FNO) [6]. The basic DeepONet approximates the operator by applying a weighted sum to the product of each of the transformed outputs from two FNN sub-networks. The upper sub-network, or branch net, is applied to the input functions while the lower trunk net is applied to the querying locations of the output function. In contrast, the FNO is a particular type of Neural Operator network [7], which accepts only input functions (not querying locations for the output) and applies a global transformation on the function input via a more intricate architecture. Motivated by fundamental solutions to partial differential equations (PDEs), the FNO network sums the output of an integral kernel transformation to the input function with the output of a linear transformation. The sum is then passed through a non-linear activation function. To accelerate the integral kernel transformation, the FNO applies a Fourier transform (FT) to the input data, with the FT of the integral kernel assumed as trainable parameters.