Predictive Limitations of Physics-Informed Neural Networks in Vortex Shedding

The recent surge of interest in physics-informed neural network (PINN) methods has led to a wave of studies that attest to their potential for solving partial differential equations (PDEs) and predicting the dynamics of physical systems. However, the predictive limitations of PINNs have not been thoroughly investigated. We look at the flow around a 2D cylinder and find that data-free PINNs are unable to predict vortex shedding. Data-driven PINN exhibits vortex shedding only while the training data (from a traditional CFD solver) is available, but reverts to the steady state solution when the data flow stops. We conducted dynamic mode decomposition and analyze the Koopman modes in the solutions obtained with PINNs versus a traditional fluid solver (PetIBM). The distribution of the Koopman eigenvalues on the complex plane suggests that PINN is numerically dispersive and diffusive. The PINN method reverts to the steady solution possibly as a consequence of spectral bias. This case study reaises concerns about the ability of PINNs to predict flows with instabilities, specifically vortex shedding. Our computational study supports the need for more theoretical work to analyze the numerical properties of PINN methods. The results in this paper are transparent and reproducible, with all data and code available in public repositories and persistent archives; links are provided in the paper repository at \url{https://github.com/barbagroup/jcs_paper_pinn}, and a Reproducibility Statement within the paper

Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration

Though PINNs (physics-informed neural networks) are now deemed as a complement to traditional CFD (computational fluid dynamics) solvers rather than a replacement, their ability to solve the Navier-Stokes equations without given data is still of great interest. This report presents our not-so-successful experiments of solving the Navier-Stokes equations with PINN as a replacement for traditional solvers. We aim to, with our experiments, prepare readers for the challenges they may face if they are interested in data-free PINN. In this work, we used two standard flow problems: 2D Taylor-Green vortex at Re=100 and 2D cylinder flow at Re=200. The PINN method solved the 2D Taylor-Green vortex problem with acceptable results, and we used this flow as an accuracy and performance benchmark. About 32 hours of training were required for the PINN method's accuracy to match the accuracy of a 16x16 finite-difference simulation, which took less than 20 seconds. The 2D cylinder flow, on the other hand, did not produce a physical solution. The PINN method behaved like a steady-flow solver and did not capture the vortex shedding phenomenon. By sharing our experience, we would like to emphasize that the PINN method is still a work-in-progress, especially in terms of solving flow problems without any given data. More work is needed to make PINN feasible for real-world problems in such applications.Comment: 8 pages, 9 figure

THE CONDUCTOR AND THE ENSEMBLE

In my experience as a beginning conductor, I encountered some difficulties with self- emotional control and conflict with the ensemble members. When I was inexperienced, it was easy for me to be nervous and tense. Sometimes I lost the ability to control my temper and facial expression and couldn't communicate with the ensemble well enough. I was aware that the interaction between the conductor and the ensemble is a key element of efficient rehearsal and for successful music making. The conductor, as the one who stands in front of people, can affect the emotional involvement of the ensemble through his attitude and personality. That is why there exists a common perception regarding the power of the conductor. Because music has such an intimate relation with emotions, the emotional involvement is very important for music making. Music can display the human being's affection unreservedly and also arouse emotionality directly. Thus, if the conductor wants the ensemble members to be able to play the interpretation of the composer's intent, he needs to demonstrate it either through his own singing voice, description, or his conducting technique. If he is able to produce the correct emotional response from the ensemble, then they can perform with the "right" feeling for each particular piece. This dissertation discusses the practical psychological methods in rehearsal, and how the conductor can earn the respect and trust of the ensemble in order to bring out the maximum influence upon his ensemble, assuming he has excellent musicality and musicianship. If the conductor knows what is the quickest and best way to inspire his ensemble and really tries to create a "psychological bridge" to his ensemble, it will be a great help for efficient rehearsal. How do the ensemble members think? In Chinese proverb, "if you want someone follow you willingly, you need to know what is his favorite and dislike, then you can earn someone's heart." In order to investigate how ensemble members perceived their conductors and related to them, I conducted a survey of 153 students participating in performing ensembles at the University of Maryland between March 28th and April 1st, 2005. I created this survey by drawing questions from my research on this topic and refining them with input with from my adviser. The appendix A of the paper includes the results of the survey

Variations of Physiological Parameters and HSP70 and HSP90 Polymorphisms in Water Buffaloes in Taiwan During Cool and Warm Season

Background: This study examined the physiological parameters of water buffaloes in Taiwan in the cool (February) and warm (August) seasons of 2020 and 2021. Methods: Data was collected for a study in February, August 2020, and 2021. The ambitious temperature, humidity, water buffaloes’ rectal temperature (RT), and respiratory rate (RR) were recorded. The plasma expression levels of heat-shock protein (HSP)70 and HSP90 were examined using an ELISA kit. Furthermore, the HSP70 and HSP90 fragment genetic sequence variations were analyzed using the PCR method and MEGA6 software. Results: The results revealed that in the warm season, the rectal temperature (RT), respiratory rate (RR), and heat tolerance coefficient (HTC) were significantly higher compared to the cool season (all P < 0.05). Additionally, the temperature-humidity index (THI) had moderate to high correlations with RT (0.518), RR (0.744), and HTC (0.757). Plasma HSP70 expression levels were higher in the warm season than in the cool season (P < 0.05). The genetic sequences of HSP70 and HSP90 fragments were compared, and five single-nucleotide variation (SNV) sites were identified. However, each genotype showed no significant physiological difference between the cool and warm seasons. Conclusion: Temperature and humidity changes in Taiwan had a significant correlation with the physical condition of water buffaloes. This information can be valuable in improving the living conditions of these animals, leading to better animal welfare. Additionally, the HSP70 and HSP90 gene variations in water buffaloes in Taiwan could be used as a reference for future research on breeding and identifying molecular markers

Aggregation Weights for Linguistic Hybrid Geometric Averaging Operator

This paper tries to point out that the aggregation weights in linguistic hybrid geometric averaging operator will dominate the final result of the ranking for alternatives. We examined the linguistic hybrid geometric averaging operator that was proposed by previous studies and found it contained several questionable results. The major defect of the previous approach was that it failed to demonstrate two core factors: accuracy and speed, both of which have been explicitly uncovered and discussed in the study. With previous work the pivotal and dominant element, distribution of weights, in finding subjectively by decision maker of linguistic hybrid geometric averaging operators for group decision-making problems, lacks solid foundation and is unjustified. Here we provide the mathematical rationale and reliable advices, to point out that deficiency. In addition, we have detected and rectified some redundancies of operational laws in the procedure of previous study due to the improper utilization of negative operators. It certainly should be noted that the careless applications of those highly dependant operators may significantly diminish the efficiency and performance of entire mechanism for decision making under fuzzy environment. We develop an easy aggregation approach based on the arithmetic mean to solve the most favorable alternative problem. A comprehensive numerical examination of 1296 tests supports our result

Pivot concept: achieving a good-quality capsulorrhexis through a 2.2 mm or less clear corneal incision by using standard capsulorhexis forceps

Letter to the edito

Biochemistry and Molecular Biology MicroRNA Signature in Wound Healing Following Excimer Laser Ablation: Role of miR-133b on TGFb1, CTGF, SMA, and COL1A1 Expression Levels in Rabbit Corneal Fibroblasts

PURPOSE. The role of microRNA (miRNA) regulation in corneal wound healing and scar formation has yet to be elucidated. This study analyzed the miRNA expression pattern involved in corneal wound healing and focused on the effect of miR-133b on expression of several profibrotic genes. METHODS. Laser-ablated mouse corneas were collected at 0 and 30 minutes and 2 days. Ribonucleic acid was collected from corneas and analyzed using cell differentiation and development miRNA PCR arrays. Luciferase assay was used to determine whether miR-133b targeted the 3 0 untranslated region (UTR) of transforming growth factor b1 (TGFb1) and connective tissue growth factor (CTGF) in rabbit corneal fibroblasts (RbCF). Quantitative realtime PCR (qRT-PCR) and Western blots were used to determine the effect of miR-133b on CTGF, smooth muscle actin (SMA), and collagen (COL1A1) in RbCF. Migration assay was used to determine the effect of miR-133b on RbCF migration. RESULTS. At day 2, 37 of 86 miRNAs had substantial expression fold changes. miR-133b had the greatest fold decrease at À14.33. Pre-miR-133b targeted the 3 0 UTR of CTGF and caused a significant decrease of 38% (P < 0.01). Transforming growth factor b1-treated RbCF had a significant decrease of miR-133b of 49% (P < 0.01), whereas CTGF, SMA, and COL1A1 had significant increases of 20%, 54%, and 37% (P < 0.01), respectively. The RbCF treated with TGFb1 and pre-miR133b showed significant decreases in expression of CTGF, SMA, and COL1A1 of 30%, 37%, and 28% (P < 0.01), respectively. Finally, there was significant decrease in migration of miR-133b-treated RbCF. CONCLUSIONS. Significant changes occur in key miRNAs during early corneal wound healing, suggesting novel miRNA targets to reduce scar formation. Keywords: CTGF, microRNA, corneal wound healing, gene expression A fter corneal trauma, stromal wound healing is the result of a complex cascade of multiple factors including growth factors, cytokines, chemokines, proteases, and, most recently discovered, microRNAs (miRNAs). Directly after epithelial damage, the process of healing is initiated by multiple cytokines and growth factors released by the epithelial cells, keratocytes/ corneal fibroblast, and/or the lacrimal gland

Emulsified Nanoparticles Containing Inactivated Influenza Virus and CpG Oligodeoxynucleotides Critically Influences the Host Immune Responses in Mice

Antigen sparing and cross-protective immunity are regarded as crucial in pandemic influenza vaccine development. Both targets can be achieved by adjuvantation strategy to elicit a robust and broadened immune response. We assessed the immunogenicity of an inactivated H5N1 whole-virion vaccine (A/Vietnam/1194/2004 NIBRG-14, clade 1) formulated with emulsified nanoparticles and investigated whether it can induce cross-clade protecting immunity.After formulation with PELC, a proprietary water-in-oil-in-water nanoemulsion comprising of bioresorbable polymer/Span(R)85/squalene, inactivated virus was intramuscularly administered to mice in either one-dose or two-dose schedule. We found that the antigen-specific serum antibody responses elicited after two doses of non-adjuvanted vaccine were lower than those observed after a single dose of adjuvanted vaccine, PELC and the conventional alum adjuvant as well. Moreover, 5 microg HA of PELC-formulated inactivated virus were capable of inducing higher antibodies than those obtained from alum-adjuvanted vaccine. In single-dose study, we found that encapsulating inactivated virus into emulsified PELC nanoparticles could induce better antibody responses than those formulated with PELC-adsorbed vaccine. However, the potency was rather reduced when the inactivated virus and CpG (an immunostimulatory oligodeoxynucleotide containing unmethylated cytosine-guanosine motifs) were co-encapsulated within the emulsion. Finally, the mice who received PELC/CpG(adsorption)-vaccine could easily and quickly reach 100% of seroprotection against a homologous virus strain and effective cross-protection against a heterologous virus strain (A/Whooper swan/Mongolia/244/2005, clade 2.2).Encapsulating inactivated H5N1 influenza virus and CpG into emulsified nanoparticles critically influences the humoral responses against pandemic influenza. These results demonstrated that the use of PELC could be as antigen-sparing in preparation for a potential shortage of prophylactic vaccines against local infectious diseases, in particular pandemic influenza. Moreover, the cross-clade neutralizing antibody responses data verify the potential of such adjuvanted H5N1 candidate vaccine as an effective tool in pre-pandemic preparedness