Physical computing systems provide a promising route toward hardware-native machine learning, but their computational capabilities remain difficult to characterize in a principled, task-independent, and data-efficient way. We extend the Information Processing Capacity (IPC) framework to stationary physical computing systems and establish several fundamental results: individual capacities are bounded between zero and one, their sum over a complete basis is bounded by the number of readouts, and noise strictly reduces this bound. We address the finite-sample estimation of IPC and derive the asymptotic form of the systematic positive bias affecting naive estimators. Building on these results, we introduce data-efficient estimation methods based on Richardson extrapolation and Sobol quasi-random sampling. We validate the framework experimentally using a photonic computing system based on picosecond laser pulses propagating through a nonlinear optical fibre. By varying the laser power and fibre length, we observe systematic shifts of the IPC distribution toward higher-order nonlinear capacities induced by the Kerr effect. Finally, we demonstrate that the total IPC strongly correlates with performance on benchmark machine-learning tasks and provides a reliable estimate of the effective dimensionality of the system. These results establish IPC as a practical bridge between the intrinsic dynamics of physical computing systems and their machine-learning performance.

Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and inverse problems of partial differential equations (PDEs) using deep learning. However they remain computationally expensive due to their iterative gradient descent based optimization and scale poorly with increasing model size. This paper introduces Physics-Informed Extreme Learning Machines (PIELMs) as fast alternative to PINNs for solving both forward and inverse problems in financial PDEs. PIELMs replace iterative optimization with a single least-squares solve, enabling deterministic and efficient training. We benchmark PIELM on the Black-Scholes and Heston-Hull-White models for forward pricing and demonstrate its capability in inverse model calibration to recover volatility and interest rate parameters from noisy data. From experiments we observe that PIELM achieve accuracy comparable to PINNs while being up to $30\times$ faster, highlighting their potential for real-time financial modeling.

Physics-informed machine learning has been a promising data-driven and physics-informed approach in geotechnical engineering. This study proposes a physics-informed extreme learning machine (PIELM) framework for analyzing tunneling-induced soil-pile interactions. The pile foundation is modeled as an Euler-Bernoulli beam, and the surrounding soil is modeled as a Pasternak foundation. The soil-pile interaction is formulated into a fourth-order ordinary differential equation (ODE) that constitutes the physics-informed component, while measured data are incorporated into PIELM as the data-driven component. Combining physics and data yields a loss vector of the extreme learning machine (ELM) network, which is trained within 1 second by the least squares method. After validating the PIELM approach by the boundary element method (BEM) and finite difference method (FDM), parametric studies are carried out to examine the effects of ELM network architecture, data monitoring locations and numbers on the performance of PIELM. The results indicate that monitored data should be placed at positions where the gradients of pile deflections are significant, such as at the pile tip/top and near tunneling zones. Two application examples highlight the critical role of physics-informed and data-driven approach for tunnelling-induced soil-pile interactions. The proposed approach shows great potential for real-time monitoring and safety assessment of pile foundations, and benefits for intelligent early-warning systems in geotechnical engineering.

A novel methodology for short-term energy forecasting using an Extreme Learning Machine ($\mathtt{ELM}$) is proposed. Using six years of hourly data collected in Corsica (France) from multiple energy sources (solar, wind, hydro, thermal, bioenergy, and imported electricity), our approach predicts both individual energy outputs and total production (including imports, which closely follow energy demand, modulo losses) through a Multi-Input Multi-Output ($\mathtt{MIMO}$) architecture. To address non-stationarity and seasonal variability, sliding window techniques and cyclic time encoding are incorporated, enabling dynamic adaptation to fluctuations. The $\mathtt{ELM}$ model significantly outperforms persistence-based forecasting, particularly for solar and thermal energy, achieving an $\mathtt{nRMSE}$ of $17.9\%$ and $5.1\%$, respectively, with $\mathtt{R^2} > 0.98$ (1-hour horizon). The model maintains high accuracy up to five hours ahead, beyond which renewable energy sources become increasingly volatile. While $\mathtt{MIMO}$ provides marginal gains over Single-Input Single-Output ($\mathtt{SISO}$) architectures and offers key advantages over deep learning methods such as $\mathtt{LSTM}$, it provides a closed-form solution with lower computational demands, making it well-suited for real-time applications, including online learning. Beyond predictive accuracy, the proposed methodology is adaptable to various contexts and datasets, as it can be tuned to local constraints such as resource availability, grid characteristics, and market structures.

Multilayer Extreme Learning Machine (ML-ELM) and its variants have proven to be an effective technique for the classification of different natural signals such as audio, video, acoustic and images. In this paper, a Hybrid Multilayer Extreme Learning Machine (HML-ELM) that is based on ELM-based autoencoder (ELM-AE) and an Interval Type-2 fuzzy Logic theory is suggested for active image classification and applied to Unmanned Aerial Vehicles (UAVs). The proposed methodology is a hierarchical ELM learning framework that consists of two main phases: 1) self-taught feature extraction and 2) supervised feature classification. First, unsupervised multilayer feature encoding is achieved by stacking a number of ELM-AEs, in which input data is projected into a number of high-level representations. At the second phase, the final features are classified using a novel Simplified Interval Type-2 Fuzzy ELM (SIT2-FELM) with a fast output reduction layer based on the SC algorithm; an improved version of the algorithm Center of Sets Type Reducer without Sorting Requirement (COSTRWSR). To validate the efficiency of the HML-ELM, two types of experiments for the classification of images are suggested. First, the HML-ELM is applied to solve a number of benchmark problems for image classification. Secondly, a number of real experiments to the active classification and transport of four different objects between two predefined locations using a UAV is implemented. Experiments demonstrate that the proposed HML-ELM delivers a superior efficiency compared to other similar methodologies such as ML-ELM, Multilayer Fuzzy Extreme Learning Machine (ML-FELM) and ELM.

Automatic food detection is an emerging topic of interest due to its wide array of applications ranging from detecting food images on social media platforms to filtering non-food photos from the users in dietary assessment apps. Recently, during the COVID-19 pandemic, it has facilitated enforcing an eating ban by automatically detecting eating activities from cameras in public places. Therefore, to tackle the challenge of recognizing food images with high accuracy, we proposed the idea of a hybrid framework for extracting and selecting optimal features from an efficient neural network. There on, a nonlinear classifier is employed to discriminate between linearly inseparable feature vectors with great precision. In line with this idea, our method extracts features from MobileNetV3, selects an optimal subset of attributes by using Shapley Additive ex-Planations (SHAP) values, and exploits kernel extreme learning machine (KELM) due to its nonlinear decision boundary and good generalization ability. However, KELM suffers from the'curse of dimensionality problem' for large datasets due to the complex computation of kernel matrix with large numbers of hidden nodes. We solved this problem by proposing a novel multicolumn kernel extreme learning machine (MCK-ELM) which exploited the k-d tree algorithm to divide data into N subsets and trains separate KELM on each subset of data. Then, the method incorporates KELM classifiers into parallel structures and selects the top k nearest subsets during testing by using the k-d tree search for classifying input instead of the whole network. Experimental results showed the superiority of our method on an integrated set of measures while solving the problem of'curse of dimensionality in KELM for large datasets. Keywords: Multicolumn, Kernel Extreme Learning Machine, MobileNet, Food Detection, Explainable AI, SHAP 1. Introduction Automatic detection of food images applications includes visual-based dietary assessment and detecting eating activities from wearable camera photos. The visual-based dietary assessment method reduces the burden of manually collecting the food data by helping users in refreshing their memory using the food pictures of the previous dietary intake. Filtering of non-food images from users is an essential step in these mHealth apps to ensure relevant images are analyzed.

Accuracy and efficiency of the conventional physics-informed neural network (PINN) need to be improved before it can be a competitive alternative for soil consolidation analyses. This paper aims to overcome these limitations by proposing a highly accurate and efficient physics-informed machine learning (PIML) approach, termed time-stepping physics-informed extreme learning machine (TS-PIELM). In the TS-PIELM framework the consolidation process is divided into numerous time intervals, which helps overcome the limitation of PIELM in solving differential equations with sharp gradients. To accelerate network training, the solution is approximated by a single-layer feedforward extreme learning machine (ELM), rather than using a fully connected neural network in PINN. The input layer weights of the ELM network are generated randomly and fixed during the training process. Subsequently, the output layer weights are directly computed by solving a system of linear equations, which significantly enhances the training efficiency compared to the time-consuming gradient descent method in PINN. Finally, the superior performance of TS-PIELM is demonstrated by solving three typical Terzaghi consolidation problems. Compared to PINN, results show that the computational efficiency and accuracy of the novel TS-PIELM framework are improved by more than 1000 times and 100 times for one-dimensional cases, respectively. This paper provides compelling evidence that PIML can be a powerful tool for computational geotechnics.

--The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to approximate the action-value function in general reinforcement learning problems. The proposed HR method ensures the provable convergence of the approximation algorithm, which makes the much-needed connection between regularization and explainable learning using neural networks. We provide lower and upper bounds for the error of the proposed HR solution, which helps build a reliable model. We also find that regularization with the proposed HR can be regarded as a contraction. We prove that the generalizability of neural networks can be maximized with a proper regularization matrix, and the proposed HR is applicable for neural networks with any mapping matrix. With the theoretical explanation of the extreme learning machine for neural network training and the proposed high-order regularization, one can better interpret the output of the neural network, thus leading to explainable learning. We present a case study based on regularized extreme learning neural networks to demonstrate the application of the proposed HR and give the corresponding incremental HR solution. We verify the performance of the proposed HR method by solving a classic control problem in reinforcement learning. The result demonstrates the superior performance of the method with significant enhancement in the generalizability of the neural network. Regularization in machine learning is often used to improve the generalizability of a neural network model; a regularization method typically imposes penalties on some properties of the model to avoid overfitting the training data and allow for better generalization to the unseen test data [1]-[3]. The penalty terms can be designed to reduce the complexity of a given model, and the accordingly obtained regularized model can have similar or even better performance [4].

--Deep neural networks (DNNs) enhance the accuracy and efficiency of reconstructing key parameters from time-resolved photon arrival signals recorded by single-photon detectors. However, the performance of conventional backpropagation-based DNNs is highly dependent on various parameters of the optical setup and biological samples under examination, necessitating frequent network retraining--either through transfer learning or from scratch. Newly collected data must also be stored and transferred to a high-performance GPU server for retraining, introducing latency and storage overhead. T o address these challenges, we propose an online training algorithm based on a One-Sided Jacobi rotation-based Online Sequential Extreme Learning Machine (OSOS-ELM). We fully exploit parallelism in executing OSOS-ELM on a heterogeneous FPGA with integrated ARM cores. Extensive evaluations of OSOS-ELM and OS-ELM demonstrate that both achieve comparable accuracy across different network dimensions (i.e., input, hidden, and output layers), while OSOS-ELM proves to be more hardware-efficient. By leveraging the parallelism of OSOS-ELM, we implement a holistic computing prototype on a Xilinx ZCU104 FPGA, which integrates a multi-core CPU and programmable logic fabric. We also implement our OSOS-ELM on the NVIDIA Jetson Xavier NX GPU to comprehensively investigate its computing performance on another type of heterogeneous computing platform. N-device training of neural networks has been emerging in recent decades. On-device training and inference save the overhead of data transfer to data centers, memory management, and computing on the cloud. The number of edge devices is increasing exponentially and is expected to reach 1 trillion by 2035 [1]. Latency tends to be a bottleneck of real-time applications such as healthcare and machine automation. Additionally, information privacy can be threatened when uploading and offloading sensitive biomedical data to the cloud. This work is supported by the EPSRC (EP/T00097X/1); the Quantum Technology Hub in Quantum Imaging (QuantiC), and the University of Strathclyde. Xingda Li also acknowledges support from China Scholarship Council.

Clearsky models are widely used in solar energy for many applications such as quality control, resource assessment, satellite-base irradiance estimation and forecasting. However, their use in forecasting and nowcasting is associated with a number of challenges. Synchronization errors, reliance on the Clearsky index (ratio of the global horizontal irradiance to its cloud-free counterpart) and high sensitivity of the clearsky model to errors in aerosol optical depth at low solar elevation limit their added value in real-time applications. This paper explores the feasibility of short-term forecasting without relying on a clearsky model. We propose a Clearsky-Free forecasting approach using Extreme Learning Machine (ELM) models. ELM learns daily periodicity and local variability directly from raw Global Horizontal Irradiance (GHI) data. It eliminates the need for Clearsky normalization, simplifying the forecasting process and improving scalability. Our approach is a non-linear adaptative statistical method that implicitely learns the irradiance in cloud-free conditions removing the need for an clear-sky model and the related operational issues. Deterministic and probabilistic results are compared to traditional benchmarks, including ARMA with McClear-generated Clearsky data and quantile regression for probabilistic forecasts. ELM matches or outperforms these methods, providing accurate predictions and robust uncertainty quantification. This approach offers a simple, efficient solution for real-time solar forecasting. By overcoming the stationarization process limitations based on usual multiplicative scheme Clearsky models, it provides a flexible and reliable framework for modern energy systems.