Project description:In this study, the applicability of physics informed neural networks using wavelets as an activation function is discussed to solve non-linear differential equations. One of the prominent equations arising in fluid dynamics namely Blasius viscous flow problem is solved. A linear coupled differential equation, a non-linear coupled differential equation, and partial differential equations are also solved in order to demonstrate the method's versatility. As the neural network's optimum design is important and is problem-specific, the influence of some of the key factors on the model's accuracy is also investigated. To confirm the approach's efficacy, the outcomes of the suggested method were compared with those of the existing approaches. The suggested method was observed to be both efficient and accurate.
Project description:Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.
Project description:Characterizing the metabolic profile of a microbial community is crucial for understanding its biological function and its impact on the host or environment. Metabolomics experiments directly measuring these profiles are difficult and expensive, while sequencing methods quantifying the species composition of microbial communities are well-developed and relatively cost-effective. Computational methods that are capable of predicting metabolomic profiles from microbial compositions can save considerable efforts needed for metabolomic profiling experimentally. Yet, despite existing efforts, we still lack a computational method with high prediction power, general applicability, and great interpretability. Here we develop a method - mNODE (Metabolomic profile predictor using Neural Ordinary Differential Equations), based on a state-of-the-art family of deep neural network models. We show compelling evidence that mNODE outperforms existing methods in predicting the metabolomic profiles of human microbiomes and several environmental microbiomes. Moreover, in the case of human gut microbiomes, mNODE can naturally incorporate dietary information to further enhance the prediction of metabolomic profiles. Besides, susceptibility analysis of mNODE enables us to reveal microbe-metabolite interactions, which can be validated using both synthetic and real data. The presented results demonstrate that mNODE is a powerful tool to investigate the microbiome-diet-metabolome relationship, facilitating future research on precision nutrition.
Project description:Physics-informed neural network has emerged as a promising approach for solving partial differential equations. However, it is still a challenge for the computation of structural mechanics problems since it involves solving higher-order partial differential equations as the governing equations are fourth-order nonlinear equations. Here we develop a multi-level physics-informed neural network framework where an aggregation model is developed by combining multiple neural networks, with each one involving only first-order or second-order partial differential equations representing different physics information such as geometrical, constitutive, and equilibrium relations of the structure. The proposed framework demonstrates a remarkable advancement over the classical neural networks in terms of the accuracy and computation time. The proposed method holds the potential to become a promising paradigm for structural mechanics computation and facilitate the intelligent computation of digital twin systems.
Project description:Systems biology tackles the challenge of understanding the high complexity in the internal regulation of homeostasis in the human body through mathematical modelling. These models can aid in the discovery of disease mechanisms and potential drug targets. However, on one hand the development and validation of knowledge-based mechanistic models is time-consuming and does not scale well with increasing features in medical data. On the other hand, data-driven approaches such as machine learning models require large volumes of data to produce generalisable models. The integration of neural networks and mechanistic models, forming universal differential equation (UDE) models, enables the automated learning of unknown model terms with less data than neural networks alone. Nevertheless, estimating parameters for these hybrid models remains difficult with sparse data and limited sampling durations that are common in biological applications. In this work, we propose the use of physiology-informed regularisation, penalising biologically implausible model behavior to guide the UDE towards more physiologically plausible regions of the solution space. In a simulation study we show that physiology-informed regularisation not only results in a more accurate forecasting of model behaviour, but also supports training with less data. We also applied this technique to learn a representation of the rate of glucose appearance in the glucose minimal model using meal response data measured in healthy people. In that case, the inclusion of regularisation reduces variability between UDE-embedded neural networks that were trained from different initial parameter guesses.
Project description:Data-driven discovery of partial differential equations (PDEs) has recently made tremendous progress, and many canonical PDEs have been discovered successfully for proof of concept. However, determining the most proper PDE without prior references remains challenging in terms of practical applications. In this work, a physics-informed information criterion (PIC) is proposed to measure the parsimony and precision of the discovered PDE synthetically. The proposed PIC achieves satisfactory robustness to highly noisy and sparse data on 7 canonical PDEs from different physical scenes, which confirms its ability to handle difficult situations. The PIC is also employed to discover unrevealed macroscale governing equations from microscopic simulation data in an actual physical scene. The results show that the discovered macroscale PDE is precise and parsimonious and satisfies underlying symmetries, which facilitates understanding and simulation of the physical process. The proposition of the PIC enables practical applications of PDE discovery in discovering unrevealed governing equations in broader physical scenes.
Project description:BackgroundIncreasing vaccination coverage was key to curbing the COVID-19 pandemic globally. However, lack of trust in the vaccine and fear of side effects in regions like the Caribbean resulted in a low uptake despite enough vaccine supply.MethodsWe conducted two correlational analyses and one experiment between five sequential behaviorally informed Facebook campaigns, social media performance outcomes, and district-level vaccination data. First, we ran multivariate linear regression models to estimate the mean differences between the campaigns in (i) social media performance ("Clicks" and "Engagement") and (ii) COVID-19 vaccination uptake at the district level. "Clicks" were measured by the number of people who clicked on the respective Facebook advert and visited the official vaccination site. "Engagements" were the number of people interacting with the advert through likes and emojis. Second, we took advantage of the experimental design during one of the campaigns to analyze the differential effect of messages conveying information about the number of people reporting vaccination side effects using words ("Few"/ "Majority) and numbers ("3 out of 100 ") on social media performance.ResultsThe correlational analysis showed that the number of "Clicks" and "Engagement\" was similar among campaigns, except for the campaign focusing on vaccines' effectiveness, which had 14.65 less clicks and 19.52 less engagements per advert (including controls and district-fixed effects) compared to the base "It's safe" campaign. Vaccination rates were highest at times coinciding with campaigns focusing on vaccination safety and effectiveness. Our experimental results showed that informational messages related to side effects that were framed using words ("Majority did not report discomfort"/ "Few persons reported discomfort") were better at generating "Clicks\" compared to those using numbers ("3 out of 100 reported discomforts").ConclusionsFacebook adverts highlighting vaccine safety had a similar level of social media performance as other campaigns, except for adverts focusing on vaccine efficacy, which performed worse. Communicating side-effect information with words instead of numbers can expand social media interest in low-uptake regions like the Caribbean. Our results serve as preliminary evidence for public health officials to encourage vaccine uptake in high-hesitancy contexts.
Project description:Background and aimsSevere influenza A(H1N1)pdm2009 virus infection cases are characterized by sustained immune activation during influenza pandemics. Seasonal flu data suggest that immune mediators could be modified by wave-related changes. Our aim was to determine the behavior of soluble and cell-related mediators in two waves at the epicenter of the 2009 influenza pandemic.MethodsLeukocyte surface activation markers were studied in serum from peripheral blood samples, collected from the 1(st) (April-May, 2009) and 2(nd) (October 2009-February 2010) pandemic waves. Patients with confirmed influenza A(H1N1)pdm2009 virus infection (H1N1), influenza-like illness (ILI) or healthy donors (H) were analyzed.ResultsSerum IL-6, IL-4 and IL-10 levels were elevated in H1N1 patients from the 2(nd) pandemic wave. Additionally, the frequency of helper and cytotoxic T cells was reduced during the 1(st) wave, whereas CD69 expression in helper T cells was increased in the 2(nd) wave for both H1N1 and ILI patients. In contrast, CD62L expression in granulocytes from the ILI group was increased in both waves but in monocytes only in the 2(nd) wave. Triggering Receptor Expressed on Myeloid cells (TREM)-1 expression was elevated only in H1N1 patients at the 1(st) wave.ConclusionsOur results show that during the 2009 influenza pandemic a T cell activation phenotype is observed in a wave-dependent fashion, with an expanded activation in the 2(nd) wave, compared to the 1(st) wave. Conversely, granulocyte and monocyte activation is infection-dependent. This evidence collected at the pandemic epicenter in 2009 could help us understand the differences in the underlying cellular mechanisms that drive the wave-related immune profile behaviors that occur against influenza viruses during pandemics.
Project description:Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for the estimated signal trajectories. We establish the estimation optimality and selection consistency of kernel ODE under both the low-dimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. Our proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA as well. We demonstrate the efficacy of our method through numerous ODE examples.
Project description:Models that are formulated as ordinary differential equations (ODEs) can accurately explain temporal gene expression patterns and promise to yield new insights into important cellular processes, disease progression, and intervention design. Learning such ODEs is challenging, since we want to predict the evolution of gene expression in a way that accurately encodes the causal gene-regulatory network (GRN) governing the dynamics and the nonlinear functional relationships between genes. Most widely used ODE estimation methods either impose too many parametric restrictions or are not guided by meaningful biological insights, both of which impedes scalability and/or explainability. To overcome these limitations, we developed PHOENIX, a modeling framework based on neural ordinary differential equations (NeuralODEs) and Hill-Langmuir kinetics, that can flexibly incorporate prior domain knowledge and biological constraints to promote sparse, biologically interpretable representations of ODEs. We test accuracy of PHOENIX in a series of in silico experiments benchmarking it against several currently used tools for ODE estimation. We also demonstrate PHOENIX's flexibility by studying oscillating expression data from synchronized yeast cells and assess its scalability by modelling genome-scale breast cancer expression for samples ordered in pseudotime. Finally, we show how the combination of user-defined prior knowledge and functional forms from systems biology allows PHOENIX to encode key properties of the underlying GRN, and subsequently predict expression patterns in a biologically explainable way.