Sirani M. Perera

Michael Trimboli, Mohammed Alsubaie, Sirani M. Perera et al.

Understanding and predicting microstructure evolution is fundamental to materials science, as it governs the resulting properties and performance of materials. Traditional simulation methods, such as phase-field models, offer high-fidelity results but are computationally expensive due to the need to solve complex partial differential equations at fine spatiotemporal resolutions. To address this challenge, we propose a deep learning-based framework that accelerates microstructure evolution predictions while maintaining high accuracy. Our approach utilizes a fully convolutional spatiotemporal model trained in a self-supervised manner using sequential images generated from simulations of microstructural processes, including grain growth and spinodal decomposition. The trained neural network effectively learns the underlying physical dynamics and can accurately capture both short-term local behaviors and long-term statistical properties of evolving microstructures, while also demonstrating generalization to unseen spatiotemporal domains and variations in configuration and material parameters. Compared to recurrent neural architectures, our model achieves state-of-the-art predictive performance with significantly reduced computational cost in both training and inference. This work establishes a robust baseline for spatiotemporal learning in materials science and offers a scalable, data-driven alternative for fast and reliable microstructure simulations.

Hansaka Aluvihare, Sivakumar Sivasankar, Xianqi Li et al.

True-time-delay (TTD) beamformers can produce wideband, squint-free beams in both analog and digital signal domains, unlike frequency-dependent FFT beams. Our previous work showed that TTD beamformers can be efficiently realized using the elements of delay Vandermonde matrix (DVM), answering the longstanding beam-squint problem. Thus, building on our work on classical algorithms based on DVM, we propose neural network (NN) architecture to realize wideband multi-beam beamformers using structure-imposed weight matrices and submatrices. The structure and sparsity of the weight matrices and submatrices are shown to reduce the space and computational complexities of the NN greatly. The proposed network architecture has O(pLM logM) complexity compared to a conventional fully connected L-layers network with O(M2L) complexity, where M is the number of nodes in each layer of the network, p is the number of submatrices per layer, and M >> p. We will show numerical simulations in the 24 GHz to 32 GHz range to demonstrate the numerical feasibility of realizing wideband multi-beam beamformers using the proposed neural architecture. We also show the complexity reduction of the proposed NN and compare that with fully connected NNs, to show the efficiency of the proposed architecture without sacrificing accuracy. The accuracy of the proposed NN architecture was shown using the mean squared error, which is based on an objective function of the weight matrices and beamformed signals of antenna arrays, while also normalizing nodes. The proposed NN architecture shows a low-complexity NN realizing wideband multi-beam beamformers in real-time for low-complexity intelligent systems.

Levi Lingsch, Mike Y. Michelis, Emmanuel de Bezenac et al.

The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids, this limits the efficiency of such neural operators when applied to problems where the input and output functions need to be processed on general non-equispaced point distributions. Leveraging the observation that a limited set of Fourier (Spectral) modes suffice to provide the required expressivity of a neural operator, we propose a simple method, based on the efficient direct evaluation of the underlying spectral transformation, to extend neural operators to arbitrary domains. An efficient implementation* of such direct spectral evaluations is coupled with existing neural operator models to allow the processing of data on arbitrary non-equispaced distributions of points. With extensive empirical evaluation, we demonstrate that the proposed method allows us to extend neural operators to arbitrary point distributions with significant gains in training speed over baselines while retaining or improving the accuracy of Fourier neural operators (FNOs) and related neural operators.

D. F. G. Coelho, R. J. Cintra, A. Madanayake et al.

This paper introduces a collection of scaling methods for generating $2N$-point DCT-II approximations based on $N$-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $2N$-point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations that outperform the transforms resulting from the JAM scaling method according to total error energy and mean squared error. Orthogonality conditions are derived and an extensive error analysis based on statistical simulation demonstrates the good performance of the introduced scaling methods. A hardware implementation is also provided demonstrating the competitiveness of the proposed methods when compared to the JAM scaling method.

Sirani M. Perera

This paper presents stable, radix-2, completely recursive discrete cosine transformation algorithms DCT-I and DCT-III solely based on DCT-I, DCT-II, DCT-III, and DCT-IV having sparse and orthogonal factors. Error bounds for computing the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having sparse and orthogonal factors are addressed. Image compression results are presented based on the recursive 2D DCT-II and DCT-IV algorithms for image size $512 \times 512$ pixels with transfer block sizes $8 \times 8$, $16 \times 16$, and $32 \times 32$ with $93.75\%$ absence of coefficients in each transfer block. Finally signal flow graphs are demonstrated based on the completely recursive DCT-I, DCT-II, DCT-III, and DCT-IV algorithms having orthogonal factors.