Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Training

In biomedical engineering, earthquake prediction, and underground energy harvesting, it is crucial to indirectly estimate the physical properties of porous media since the direct measurement of those are usually impractical/prohibitive. Here we apply the physics-informed neural networks to solve the inverse problem with regard to the nonlinear Biot's equations. Specifically, we consider batch training and explore the effect of different batch sizes. The results show that training with small batch sizes, i.e., a few examples per batch, provides better approximations (lower percentage error) of the physical parameters than using large batches or the full batch. The increased accuracy of the physical parameters, comes at the cost of longer training time. Specifically, we find the size should not be too small since a very small batch size requires a very long training time without a corresponding improvement in estimation accuracy. We find that a batch size of 8 or 32 is a good compromise, which is also robust to additive noise in the data. The learning rate also plays an important role and should be used as a hyperparameter.Comment: arXiv admin note: text overlap with arXiv:2002.0823

MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework

We propose MeshfreeFlowNet, a novel deep learning-based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, MeshfreeFlowNet accurately recovers the fine-scale quantities of interest. MeshfreeFlowNet allows for: (i) the output to be sampled at all spatio-temporal resolutions, (ii) a set of Partial Differential Equation (PDE) constraints to be imposed, and (iii) training on fixed-size inputs on arbitrarily sized spatio-temporal domains owing to its fully convolutional encoder. We empirically study the performance of MeshfreeFlowNet on the task of super-resolution of turbulent flows in the Rayleigh-Benard convection problem. Across a diverse set of evaluation metrics, we show that MeshfreeFlowNet significantly outperforms existing baselines. Furthermore, we provide a large scale implementation of MeshfreeFlowNet and show that it efficiently scales across large clusters, achieving 96.80% scaling efficiency on up to 128 GPUs and a training time of less than 4 minutes.Comment: Supplementary Video: https://youtu.be/mjqwPch9gDo. Accepted to SC2

Fuzzy-logic-based control, filtering, and fault detection for networked systems: A Survey

This paper is concerned with the overview of the recent progress in fuzzy-logic-based filtering, control, and fault detection problems. First, the network technologies are introduced, the networked control systems are categorized from the aspects of fieldbuses and industrial Ethernets, the necessity of utilizing the fuzzy logic is justified, and the network-induced phenomena are discussed. Then, the fuzzy logic control strategies are reviewed in great detail. Special attention is given to the thorough examination on the latest results for fuzzy PID control, fuzzy adaptive control, and fuzzy tracking control problems. Furthermore, recent advances on the fuzzy-logic-based filtering and fault detection problems are reviewed. Finally, conclusions are given and some possible future research directions are pointed out, for example, topics on two-dimensional networked systems, wireless networked control systems, Quality-of-Service (QoS) of networked systems, and fuzzy access control in open networked systems.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374039, 61473163, and 61374127, the Hujiang Foundation of China under Grants C14002 andD15009, the Engineering and Physical Sciences Research Council (EPSRC) of the UK, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany