Information on natural phenomena and engineering systems is typically contained in data. Data can be corrupted by systematic errors in models and experiments. In this paper, we propose a tool to uncover the spatiotemporal solution of the underlying physical system by removing the systematic errors from data. The tool is the physics-constrained convolutional neural network (PC-CNN), which combines information from both the systems governing equations and data. We focus on fundamental phenomena that are modelled by partial differential equations, such as linear convection, Burgers equation, and two-dimensional turbulence. First, we formulate the problem, describe the physics-constrained convolutional neural network, and parameterise the systematic error. Second, we uncover the solutions from data corrupted by large multimodal systematic errors. Third, we perform a parametric study for different systematic errors. We show that the method is robust. Fourth, we analyse the physical properties of the uncovered solutions. We show that the solutions inferred from the PC-CNN are physical, in contrast to the data corrupted by systematic errors that does not fulfil the governing equations. This work opens opportunities for removing epistemic errors from models, and systematic errors from measurements.

Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects become important and a turbulence closure is required, and in systems with a large Knudsen number, kinetic effects become important and a kinetic closure is required. By adding an equation governing the growth and transport of the quantity requiring the closure relation, it becomes possible to capture microphysics through the introduction of ``hidden variables'' that are non-local in space and time. The behavior of the ``hidden variables'' in response to the fluid conditions can be learned from a higher fidelity or ab-initio model that contains all the microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks against ground-truth simulations. We show that this method enables an Euler equation based approach to reproduce non-linear, large Knudsen number plasma physics that can otherwise only be modeled using Boltzmann-like equation simulators such as Vlasov or Particle-In-Cell modeling.

The use of machine learning (ML) Michalski et al (2013); LeCun et al (2015) methods in material science to accelerate materials discoveryCurtarolo et al (2013) is at the base of the so-called material informatics (MI) Ramakrishna et al (2019); Ramprasad et al (2017); Takahashi and Tanaka (2016); L. Ward (2017); Rajan (2005). By training ML models on large databases, such as OQMD or the Materials Project high-throughput electronic structure calculation databases Saal et al (2013); Jain et al (2013); Curtarolo (2012); Hachmann et al (2011); NOMAD (https://nomad-coe.eu), the goal is to achieve predictions of material properties with quantum accuracy. As in statistical mechanics with the need for identifying appropriate order parameters of novel phases and structures, the key challenge in ML algorithms is to identify effective system descriptors that can function as structure identifiers. A large variety of descriptors have been proposed, including fixed-length feature vectors of material elemental or electronic properties Seko et al (2015); Xue et al (2016); Isayev et al (2017), as well as structural descriptors, based on rotational and traslational invariant transformations of atomic coordinates, like the Coulomb matrix Rupp et al (2012), atom-centered symmetry functions (ACSFs) Behler (2011), social permutation invariant coordintes (SPRINT) Pietrucci and Andreoni (2011), smooth overlap of atomic positions (SOAP) De et al (2016) and global minimum of root mean-square distance Sadeghi et al (2013). However, these solutions are often system-specific, and are not suitable for vast compositional and structural space exploration.

Transformer-based language models have achieved remarkable success in few-shot in-context learning and drawn a lot of research interest. However, these models' performance greatly depends on the choice of the example prompts and also has high variability depending on how samples are chosen. In this paper, we conduct a comprehensive study of retrieving semantically similar few-shot samples and using them as the context, as it helps the model decide the correct label without any gradient update in the multilingual and cross-lingual settings. We evaluate the proposed method on five natural language understanding datasets related to intent detection, question classification, sentiment analysis, and topic classification. The proposed method consistently outperforms random sampling in monolingual and cross-lingual tasks in non-English languages.

Many neural architectures such as fully-connected, convolutional and recurrent neural networks were developed and tested on public datasets such as NASA C-MAPSS, Case Western Reserve University Bearings and FEMTO Bearings datasets to diagnose equipment health state and/or predict the remaining useful life (RUL) before breakdown. Many data processing and feature extraction procedures were used in combination with deep learning techniques such as dimensionality reduction (Principal Component Analysis) and signal processing (Fourier and Wavelet analyses) in order to create more meaningful and robust features to use as an input for neural networks architectures. This thesis also explored the potential use of these techniques in predictive maintenance within oil rigs for monitoring oilfield critical equipment in order to reduce unpredicted downtime and maintenance costs.

Muscle health is a critical component of overall health and quality of life. However, current measures of skeletal muscle health take limited account of microstructural variations within muscle, which play a crucial role in mediating muscle function. To address this, we present a physics-inspired, machine learning-based framework for the non-invasive and in vivo estimation of microstructural organization in skeletal muscle from diffusion-weighted MRI (dMRI). To reduce the computational expense associated with direct numerical simulations of dMRI physics, a polynomial meta-model is developed that accurately represents the input/output relationships of a high-fidelity numerical model. This meta-model is used to develop a Gaussian process (GP) model to provide voxel-wise estimates and confidence intervals of microstructure organization in skeletal muscle. Given noise-free data, the GP model accurately estimates microstructural parameters. In the presence of noise, the diameter, intracellular diffusion coefficient, and membrane permeability are accurately estimated with narrow confidence intervals, while volume fraction and extracellular diffusion coefficient are poorly estimated and exhibit wide confidence intervals. A reduced-acquisition GP model, consisting of one-third the diffusion-encoding measurements, is shown to predict parameters with similar accuracy to the original model. The fiber diameter and volume fraction estimated by the reduced GP model is validated via histology, with both parameters within their associated confidence intervals, demonstrating the capability of the proposed framework as a promising non-invasive tool for assessing skeletal muscle health and function.

Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image, protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly deep learning (DL), applied and relevant to computational mechanics (solid, fluids, finite-element technology) are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. Hybrid methods combine traditional PDE discretizations with ML methods either (1) to help model complex nonlinear constitutive relations, (2) to nonlinearly reduce the model order for efficient simulation (turbulence), or (3) to accelerate the simulation by predicting certain components in the traditional integration methods. Here, methods (1) and (2) relied on Long-Short-Term Memory (LSTM) architecture, with method (3) relying on convolutional neural networks. Pure ML methods to solve (nonlinear) PDEs are represented by Physics-Informed Neural network (PINN) methods, which could be combined with attention mechanism to address discontinuous solutions. Both LSTM and attention architectures, together with modern and generalized classic optimizers to include stochasticity for DL networks, are extensively reviewed. Kernel machines, including Gaussian processes, are provided to sufficient depth for more advanced works such as shallow networks with infinite width. Not only addressing experts, readers are assumed familiar with computational mechanics, but not with DL, whose concepts and applications are built up from the basics, aiming at bringing first-time learners quickly to the forefront of research. History and limitations of AI are recounted and discussed, with particular attention at pointing out misstatements or misconceptions of the classics, even in well-known references. Positioning and pointing control of a large-deformable beam is given as an example.

Achieving the economical and stable operation of Multi-microgrids (MMG) systems is vital. However, there are still some challenging problems to be solved. Firstly, from the perspective of stable operation, it is necessary to minimize the energy fluctuation of the main grid. Secondly, the characteristics of energy conversion equipment need to be considered. Finally, privacy protection while reducing the operating cost of an MMG system is crucial. To address these challenges, a Data-driven strategy for MMG systems with Shared Energy Storage (SES) is proposed. The Mixed-Attention is applied to fit the conditions of the equipment, additionally, Multi-Agent Soft Actor-Critic(MA-SAC) and (Multi-Agent Win or Learn Fast Policy Hill-Climbing)MA-WoLF-PHC are proposed to solve the partially observable dynamic stochastic game problem. By testing the operation data of the MMG system in Northwest China, following conclusions are drawn: the R-Square (R2) values of results reach 0.999, indicating the neural network effectively models the nonlinear conditions. The proposed MMG system framework can reduce energy fluctuations in the main grid by 1746.5kW in 24 hours and achieve a cost reduction of 16.21% in the test. Finally, the superiority of the proposed algorithms is verified through their fast convergence speed and excellent optimization performance.

An efficient characterization of scientifically significant locations is essential prior to the return of humans to the Moon. The highest resolution imagery acquired from orbit of south-polar shadowed regions and other relevant locations remains, at best, an order of magnitude larger than the characteristic length of most of the robotic systems to be deployed. This hinders the planning and successful implementation of prospecting missions and poses a high risk for the traverse of robots and humans, diminishing the potential overall scientific and commercial return of any mission. We herein present the design of a lightweight, compact, autonomous, and reusable lunar reconnaissance drone capable of assisting other ground-based robotic assets, and eventually humans, in the characterization and high-resolution mapping (~0.1 m/px) of particularly challenging and hard-to-access locations on the lunar surface. The proposed concept consists of two main subsystems: the drone and its service station. With a total combined wet mass of 100 kg, the system is capable of 11 flights without refueling the service station, enabling almost 9 km of accumulated flight distance. The deployment of such a system could significantly impact the efficiency of upcoming exploration missions, increasing the distance covered per day of exploration and significantly reducing the need for recurrent contacts with ground stations on Earth.

Mid-term electricity load forecasting (LF) plays a critical role in power system planning and operation. To address the issue of error accumulation and transfer during the operation of existing LF models, a novel model called error correction based LF (ECLF) is proposed in this paper, which is designed to provide more accurate and stable LF. Firstly, time series analysis and feature engineering act on the original data to decompose load data into three components and extract relevant features. Then, based on the idea of stacking ensemble, long short-term memory is employed as an error correction module to forecast the components separately, and the forecast results are treated as new features to be fed into extreme gradient boosting for the second-step forecasting. Finally, the component sub-series forecast results are reconstructed to obtain the final LF results. The proposed model is evaluated on real-world electricity load data from two cities in China, and the experimental results demonstrate its superior performance compared to the other benchmark models.