Bi-level Physics-Informed Neural Networks for PDE Constrained Optimization using Broyden's Hypergradients

Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, existing methods are insufficient to handle those PDE constraints that have a complicated or nonlinear dependency on optimization targets. In this paper, we present a novel bi-level optimization framework to resolve the challenge by decoupling the optimization of the targets and constraints. For the inner loop optimization, we adopt PINNs to solve the PDE constraints only. For the outer loop, we design a novel method by using Broyden's method based on the Implicit Function Theorem (IFT), which is efficient and accurate for approximating hypergradients. We further present theoretical explanations and error analysis of the hypergradients computation. Extensive experiments on multiple large-scale and nonlinear PDE constrained optimization problems demonstrate that our method achieves state-of-the-art results compared with strong baselines

A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs

We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first introduce the "extra fields" from the mixed finite element method to reformulate the PDEs so as to equivalently transform the three types of BCs into linear forms. Based on the reformulation, we derive the general solutions of the BCs analytically, which are employed to construct an ansatz that automatically satisfies the BCs. With such a framework, we can train the neural networks without adding extra loss terms and thus efficiently handle geometrically complex PDEs, alleviating the unbalanced competition between the loss terms corresponding to the BCs and PDEs. We theoretically demonstrate that the "extra fields" can stabilize the training process. Experimental results on real-world geometrically complex PDEs showcase the effectiveness of our method compared with state-of-the-art baselines.Comment: 10 pages, 6 figures, NeurIPS 202

Task Aware Dreamer for Task Generalization in Reinforcement Learning

A long-standing goal of reinforcement learning is to acquire agents that can learn on training tasks and generalize well on unseen tasks that may share a similar dynamic but with different reward functions. A general challenge is to quantitatively measure the similarities between these different tasks, which is vital for analyzing the task distribution and further designing algorithms with stronger generalization. To address this, we present a novel metric named Task Distribution Relevance (TDR) via optimal Q functions of different tasks to capture the relevance of the task distribution quantitatively. In the case of tasks with a high TDR, i.e., the tasks differ significantly, we show that the Markovian policies cannot differentiate them, leading to poor performance. Based on this insight, we encode all historical information into policies for distinguishing different tasks and propose Task Aware Dreamer (TAD), which extends world models into our reward-informed world models to capture invariant latent features over different tasks. In TAD, we calculate the corresponding variational lower bound of the data log-likelihood, including a novel term to distinguish different tasks via states, to optimize reward-informed world models. Extensive experiments in both image-based control tasks and state-based control tasks demonstrate that TAD can significantly improve the performance of handling different tasks simultaneously, especially for those with high TDR, and demonstrate a strong generalization ability to unseen tasks

Structural study in Highly Compressed BiFeO3 Epitaxial Thin Films on YAlO3

We report a study on the thermodynamic stability and structure analysis of the epitaxial BiFeO3 (BFO) thin films grown on YAlO3 (YAO) substrate. First we observe a phase transition of MC-MA-T occurs in thin sample (<60 nm) with an utter tetragonal-like phase (denoted as MII here) with a large c/a ratio (~1.23). Specifically, MII phase transition process refers to the structural evolution from a monoclinic MC structure at room temperature to a monoclinic MA at higher temperature (150oC) and eventually to a presence of nearly tetragonal structure above 275oC. This phase transition is further confirmed by the piezoforce microscopy measurement, which shows the rotation of polarization axis during the phase transition. A systematic study on structural evolution with thickness to elucidate the impact of strain state is performed. We note that the YAO substrate can serve as a felicitous base for growing T-like BFO because this phase stably exists in very thick film. Thick BFO films grown on YAO substrate exhibit a typical "morphotropic-phase-boundary"-like feature with coexisting multiple phases (MII, MI, and R) and a periodic stripe-like topography. A discrepancy of arrayed stripe morphology in different direction on YAO substrate due to the anisotropic strain suggests a possibility to tune the MPB-like region. Our study provides more insights to understand the strain mediated phase co-existence in multiferroic BFO system.Comment: 18 pages, 6 figures, submitted to Journal of Applied Physic

Successful treatment of methemoglobinemia in an elderly couple with severe cyanosis: two case reports

INTRODUCTION: Methemoglobinemia should be considered in all cyanotic patients who remain unresponsive to oxygen therapy. Rapid diagnosis is very important in emergency cases. Here, we present the cases of two patients, a married couple, admitted to our hospital with methemoglobinemia after exposure to sodium nitrite. CASE PRESENTATION: Two patients, a married couple, presented with methemoglobinemia. The 72-year-old Taiwanese man and 68-year-old Taiwanese woman were referred to our hospital with dizziness and tachypnea. On examination, their mucous membranes were cyanotic, and their blood samples showed the classic ‘chocolate brown’ appearance. The man also reported having experienced twitching of his right arm for a few minutes before arrival at the hospital. The symptoms of both patients failed to improve in response to supplemental oxygen delivered via oxygen masks, although the arterial blood gas data of these patients were normal and their pulse oximetry showed oxyhemoglobin levels of approximately 85%. A carbon monoxide-oximeter showed that the man’s methemoglobin concentration was 48.3%, and the woman’s was 36.4%. Methylene blue (100mg) was administered intravenously to both patients, and their symptoms improved dramatically. They were admitted to the intensive care unit and discharged three days later, without neurological sequelae. CONCLUSION: Severe methemoglobinemia is a life-threatening condition and, if untreated, may result in death. Early diagnosis and appropriate antidotal treatment are crucial in treating this emergency situation

Role of TRPM8 in dorsal root ganglion in nerve injury-induced chronic pain

<p>Abstract</p> <p>Background</p> <p>Chronic neuropathic pain is an intractable pain with few effective treatments. Moderate cold stimulation can relieve pain, and this may be a novel train of thought for exploring new methods of analgesia. Transient receptor potential melastatin 8 (TRPM8) ion channel has been proposed to be an important molecular sensor for cold. Here we investigate the role of TRPM8 in the mechanism of chronic neuropathic pain using a rat model of chronic constriction injury (CCI) to the sciatic nerve.</p> <p>Results</p> <p>Mechanical allodynia, cold and thermal hyperalgesia of CCI rats began on the 4th day following surgery and maintained at the peak during the period from the 10th to 14th day after operation. The level of TRPM8 protein in L5 dorsal root ganglion (DRG) ipsilateral to nerve injury was significantly increased on the 4th day after CCI, and reached the peak on the 10th day, and remained elevated on the 14th day following CCI. This time course of the alteration of TRPM8 expression was consistent with that of CCI-induced hyperalgesic response of the operated hind paw. Besides, activation of cold receptor TRPM8 of CCI rats by intrathecal application of menthol resulted in the inhibition of mechanical allodynia and thermal hyperalgesia and the enhancement of cold hyperalgesia. In contrast, downregulation of TRPM8 protein in ipsilateral L5 DRG of CCI rats by intrathecal TRPM8 antisense oligonucleotide attenuated cold hyperalgesia, but it had no effect on CCI-induced mechanical allodynia and thermal hyperalgesia.</p> <p>Conclusions</p> <p>TRPM8 may play different roles in mechanical allodynia, cold and thermal hyperalgesia that develop after nerve injury, and it is a very promising research direction for the development of new therapies for chronic neuroapthic pain.</p