Operator learning has become a powerful tool in machine learning for modeling complex physical systems. Although Deep Operator Networks (DeepONet) show promise, they require extensive data acquisition. Physics-informed DeepONets (PI-DeepONet) mitigate data scarcity but suffer from inefficient training processes. We introduce Separable Operator Networks (SepONet), a novel framework that significantly enhances the efficiency of physics-informed operator learning. SepONet uses independent trunk networks to learn basis functions separately for different coordinate axes, enabling faster and more memory-efficient training via forward-mode automatic differentiation. We provide theoretical guarantees for SepONet using the universal approximation theorem and validate its performance through comprehensive benchmarking against PI-DeepONet. Our results demonstrate that for the 1D time-dependent advection equation, when targeting a mean relative $\ell_{2}$ error of less than 6% on 100 unseen variable coefficients, SepONet provides up to $112 \times$ training speed-up and $82 \times$ GPU memory usage reduction compared to PI-DeepONet. Similar computational advantages are observed across various partial differential equations, with SepONet's efficiency gains scaling favorably as problem complexity increases. This work paves the way for extreme-scale learning of continuous mappings between infinite-dimensional function spaces.

However, the prediction of crude oil prices is renowned for its obscurity and complexity. The high degree of volatility, unpredictable, irregular events, and complex interconnections among market factors make it extremely challenging to accurately forecast the fluctuations in crude oil prices. The dynamic interplay of supply and demand and changes in oil prices are influenced by external factors such as economic growth, financial markets, geopolitical conflicts, warfare, and political considerations [1, 2, 3]. A variety of methodologies have been utilised for predicting crude oil prices, involving the application of econometric and statistical time series analysis techniques such as VAR [4], ARIMA, GARCH [5], VMD [6], and Walvet decomposition [7]. In more recent studies, there has been a prevalent use of machine learning models and hybrid approaches [2, 8, 9] in the literature. Nevertheless, achieving accurate oil price forecasting remains a challenging task, particularly in terms of multi-step forecasting. Traditional econometric and statistical methods are often inadequate for forecasting oil prices due to many challenges related to the irregular characteristics of energy markets, such as non-stationarity, multi-frequency, non-linearity, and chaotic properties [10].

Accurate crude oil price forecasting is crucial for various economic activities, including energy trading, risk management, and investment planning. Although deep learning models have emerged as powerful tools for crude oil price forecasting, achieving accurate forecasts remains challenging. Deep learning models' performance is heavily influenced by hyperparameters tuning, and they are expected to perform differently under various circumstances. Furthermore, price volatility is also sensitive to external factors such as world events. To address these limitations, we propose a hybrid approach combining metaheuristic optimisation and an ensemble of five popular neural network architectures used in time series forecasting. Unlike existing methods that apply metaheuristics to optimise hyperparameters within the neural network architecture, we exploit the GWO metaheuristic optimiser at four levels: feature selection, data preparation, model training, and forecast blending. The proposed approach has been evaluated for forecasting three-ahead days using real-world Brent crude oil price data, and the obtained results demonstrate that the proposed approach improves the forecasting performance measured using various benchmarks, achieving 0.000127 of MSE.

Personalized 3D avatars require an animatable representation of digital humans. Doing so instantly from monocular videos offers scalability to broad class of users and wide-scale applications. In this paper, we present a fast, simple, yet effective method for creating animatable 3D digital humans from monocular videos. Our method utilizes the efficiency of Gaussian splatting to model both 3D geometry and appearance. However, we observed that naively optimizing Gaussian splats results in inaccurate geometry, thereby leading to poor animations. This work achieves and illustrates the need of accurate 3D mesh-type modelling of the human body for animatable digitization through Gaussian splats. This is achieved by developing a novel pipeline that benefits from three key aspects: (a) implicit modelling of surface's displacements and the color's spherical harmonics; (b) binding of 3D Gaussians to the respective triangular faces of the body template; (c) a novel technique to render normals followed by their auxiliary supervision. Our exhaustive experiments on three different benchmark datasets demonstrates the state-of-the-art results of our method, in limited time settings. In fact, our method is faster by an order of magnitude (in terms of training time) than its closest competitor. At the same time, we achieve superior rendering and 3D reconstruction performance under the change of poses.

We introduce, Q-Sparse, a simple yet effective approach to training sparsely-activated large language models (LLMs). Q-Sparse enables full sparsity of activations in LLMs which can bring significant efficiency gains in inference. This is achieved by applying top-K sparsification to the activations and the straight-through-estimator to the training. The key results from this work are, (1) Q-Sparse can achieve results comparable to those of baseline LLMs while being much more efficient at inference time; (2) We present an inference-optimal scaling law for sparsely-activated LLMs; (3) Q-Sparse is effective in different settings, including training-from-scratch, continue-training of off-the-shelf LLMs, and finetuning; (4) Q-Sparse works for both full-precision and 1-bit LLMs (e.g., BitNet b1.58). Particularly, the synergy of BitNet b1.58 and Q-Sparse (can be equipped with MoE) provides the cornerstone and a clear path to revolutionize the efficiency, including cost and energy consumption, of future LLMs.

Hybrid intelligence aims to enhance decision-making, problem-solving, and overall system performance by combining the strengths of both, human cognitive abilities and artificial intelligence. With the rise of Large Language Models (LLM), progressively participating as smart agents to accelerate machine learning development, Hybrid Intelligence is becoming an increasingly important topic for effective interaction between humans and machines. This paper presents an approach to leverage Hybrid Intelligence towards sustainable and energy-aware machine learning. When developing machine learning models, final model performance commonly rules the optimization process while the efficiency of the process itself is often neglected. Moreover, in recent times, energy efficiency has become equally crucial due to the significant environmental impact of complex and large-scale computational processes. The contribution of this work covers the interactive inclusion of secondary knowledge sources through Human-in-the-loop (HITL) and LLM agents to stress out and further resolve inefficiencies in the machine learning development process.

Diffusion models generate new samples by progressively decreasing the noise from the initially provided random distribution. This inference procedure generally utilizes a trained neural network numerous times to obtain the final output, creating significant latency and energy consumption on digital electronic hardware such as GPUs. In this study, we demonstrate that the propagation of a light beam through a semi-transparent medium can be programmed to implement a denoising diffusion model on image samples. This framework projects noisy image patterns through passive diffractive optical layers, which collectively only transmit the predicted noise term in the image. The optical transparent layers, which are trained with an online training approach, backpropagating the error to the analytical model of the system, are passive and kept the same across different steps of denoising. Hence this method enables high-speed image generation with minimal power consumption, benefiting from the bandwidth and energy efficiency of optical information processing.

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for approximating nonlinear PDEs, the majority of these methods neglect fundamental physical laws and lack interpretability. We address these shortcomings by introducing Physics-embedded Fourier Neural Networks (PeFNN) with flexible and explainable error control. PeFNN is designed to enforce momentum conservation and yields interpretable nonlinear expressions by utilizing unique multi-scale momentum-conserving Fourier (MC-Fourier) layers and an element-wise product operation. The MC-Fourier layer is by design translation- and rotation-invariant in the frequency domain, serving as a plug-and-play module that adheres to the laws of momentum conservation. PeFNN establishes a new state-of-the-art in solving widely employed spatiotemporal PDEs and generalizes well across input resolutions. Further, we demonstrate its outstanding performance for challenging real-world applications such as large-scale flood simulations.

Deep Learning Architectures employ heavy computations and bulk of the computational energy is taken up by the convolution operations in the Convolutional Neural Networks. The objective of our proposed work is to reduce the energy consumption and size of CNN for using machine learning techniques in edge computing on ubiquitous computing devices. We propose Systematic Quality Scalable Design Methodology consisting of Quality Scalable Quantization on a higher abstraction level and Quality Scalable Multipliers at lower abstraction level. The first component consists of parameter compression where we approximate representation of values in filters of deep learning models by encoding in 3 bits. A shift and scale based on-chip decoding hardware is proposed which can decode these 3-bit representations to recover approximate filter values. The size of the DNN model is reduced this way and can be sent over a communication channel to be decoded on the edge computing devices. This way power is reduced by limiting data bits by approximation. In the second component we propose a quality scalable multiplier which reduces the number of partial products by converting numbers in canonic sign digit representations and further approximating the number by reducing least significant bits. These quantized CNNs provide almost same ac-curacy as network with original weights with little or no fine-tuning. The hardware for the adaptive multipliers utilize gate clocking for reducing energy consumption during multiplications. The proposed methodology greatly reduces the memory and power requirements of DNN models making it a feasible approach to deploy Deep Learning on edge computing. The experiments done on LeNet and ConvNets show an increase upto 6% of zeros and memory savings upto 82.4919% while keeping the accuracy near the state of the art.

We present an autonomous exploration system for efficient coverage of unknown environments. First, a rapid environment preprocessing method is introduced to provide environmental information for subsequent exploration planning. Then, the whole exploration space is divided into multiple subregion cells, each with varying levels of detail. The subregion cells are capable of decomposition and updating online, effectively characterizing dynamic unknown regions with variable resolution. Finally, the hierarchical planning strategy treats subregions as basic planning units and computes an efficient global coverage path. Guided by the global path, the local path that sequentially visits the viewpoint set is refined to provide an executable path for the robot. This hierarchical planning from coarse to fine steps reduces the complexity of the planning scheme while improving exploration efficiency. The proposed method is compared with state-of-art methods in benchmark environments. Our approach demonstrates superior efficiency in completing exploration while using lower computational resources.