Project description:We propose a discretization-free approach to simulation of cyclic voltammetry using Physics-Informed Neural Networks (PINNs) by constraining a feed-forward neutral network with the diffusion equation and electrochemically consistent boundary conditions. Using PINNs, we first predict one-dimensional voltammetry at a disc electrode with semi-infinite or thin layer boundary conditions. The voltammograms agree quantitatively with those obtained independently using the finite difference method and/or previously reported analytical expressions. Further, we predict the voltammetry at a microband electrode, solving the two-dimensional diffusion equation, obtaining results in close agreement with the literature. Last, we apply a PINN to voltammetry at the edges of a square electrode, quantifying the nonuniform current distribution near the corner of electrode. In general, we noticed the relative ease of developing PINNs for the solution of, in particular, the higher dimensional problem, and recommend PINNs as a potentially faster and easier alternative to existing approaches for voltammetric problems.
Project description:The inverse protein folding problem, also known as protein sequence design, seeks to predict an amino acid sequence that folds into a specific structure and performs a specific function. Recent advancements in machine learning techniques have been successful in generating functional sequences, outperforming previous energy function-based methods. However, these machine learning methods are limited in their interoperability and robustness, especially when designing proteins that must function under non-ambient conditions, such as high temperature, extreme pH, or in various ionic solvents. To address this issue, we propose a new Physics-Informed Neural Networks (PINNs)-based protein sequence design approach. Our approach combines all-atom molecular dynamics simulations, a PINNs MD surrogate model, and a relaxation of binary programming to solve the protein design task while optimizing both energy and the structural stability of proteins. We demonstrate the effectiveness of our design framework in designing proteins that can function under non-ambient conditions.
Project description:Building reduced-order models (ROMs) is essential for efficient forecasting and control of complex dynamical systems. Recently, autoencoder-based methods for building such models have gained significant traction, but their demand for data limits their use when the data is scarce and expensive. We propose aiding a model's training with the knowledge of physics using a collocation-based physics-informed loss term. Our innovation builds on ideas from classical collocation methods of numerical analysis to embed knowledge from a known equation into the latent-space dynamics of a ROM. We show that the addition of our physics-informed loss allows for exceptional data supply strategies that improves the performance of ROMs in data-scarce settings, where training high-quality data-driven models is impossible. Namely, for a problem of modeling a high-dimensional nonlinear PDE, our experiments show [Formula: see text] 5 performance gains, measured by prediction error, in a low-data regime, [Formula: see text] 10 performance gains in tasks of high-noise learning, [Formula: see text] 100 gains in the efficiency of utilizing the latent-space dimension, and [Formula: see text] 200 gains in tasks of far-out out-of-distribution forecasting relative to purely data-driven models. These improvements pave the way for broader adoption of network-based physics-informed ROMs in compressive sensing and control applications.
Project description:Physics informed neural networks have been gaining popularity due to their unique ability to incorporate physics laws into data-driven models, ensuring that the predictions are not only consistent with empirical data but also align with domain-specific knowledge in the form of physics equations. The integration of physics principles enables the method to require less data while maintaining the robustness of deep learning in modelling complex dynamical systems. However, current PINN frameworks are not sufficiently mature for real-world ODE systems, especially those with extreme multi-scale behavior such as mosquito population dynamical modelling. In this research, we propose a PINN framework with several improvements for forward and inverse problems for ODE systems with a case study application in modelling the dynamics of mosquito populations. The framework tackles the gradient imbalance and stiff problems posed by mosquito ordinary differential equations. The method offers a simple but effective way to resolve the time causality issue in PINNs by gradually expanding the training time domain until it covers entire domain of interest. As part of a robust evaluation, we conduct experiments using simulated data to evaluate the effectiveness of the approach. Preliminary results indicate that physics-informed machine learning holds significant potential for advancing the study of ecological systems.
Project description:Accurately inferring underlying electrophysiological (EP) tissue properties from action potential recordings is expected to be clinically useful in the diagnosis and treatment of arrhythmias such as atrial fibrillation. It is, however, notoriously difficult to perform. We present EP-PINNs (Physics Informed Neural Networks), a novel tool for accurate action potential simulation and EP parameter estimation from sparse amounts of EP data. We demonstrate, using 1D and 2D in silico data, how EP-PINNs are able to reconstruct the spatio-temporal evolution of action potentials, whilst predicting parameters related to action potential duration (APD), excitability and diffusion coefficients. EP-PINNs are additionally able to identify heterogeneities in EP properties, making them potentially useful for the detection of fibrosis and other localised pathology linked to arrhythmias. Finally, we show EP-PINNs effectiveness on biological in vitro preparations, by characterising the effect of anti-arrhythmic drugs on APD using optical mapping data. EP-PINNs are a promising clinical tool for the characterisation and potential treatment guidance of arrhythmias.
Project description:BackgroundExisting feature selection methods typically do not consider prior knowledge in the form of structural relationships among features. In this study, the features are structured based on prior knowledge into groups. The problem addressed in this article is how to select one representative feature from each group such that the selected features are jointly discriminating the classes. The problem is formulated as a binary constrained optimization and the combinatorial optimization is relaxed as a convex-concave problem, which is then transformed into a sequence of convex optimization problems so that the problem can be solved by any standard optimization algorithm. Moreover, a block coordinate gradient descent optimization algorithm is proposed for high dimensional feature selection, which in our experiments was four times faster than using a standard optimization algorithm.ResultsIn order to test the effectiveness of the proposed formulation, we used microarray analysis as a case study, where genes with similar expressions or similar molecular functions were grouped together. In particular, the proposed block coordinate gradient descent feature selection method is evaluated on five benchmark microarray gene expression datasets and evidence is provided that the proposed method gives more accurate results than the state-of-the-art gene selection methods. Out of 25 experiments, the proposed method achieved the highest average AUC in 13 experiments while the other methods achieved higher average AUC in no more than 6 experiments.ConclusionA method is developed to select a feature from each group. When the features are grouped based on similarity in gene expression, we showed that the proposed algorithm is more accurate than state-of-the-art gene selection methods that are particularly developed to select highly discriminative and less redundant genes. In addition, the proposed method can exploit any grouping structure among features, while alternative methods are restricted to using similarity based grouping.
Project description:In materials science, accurately computing properties like viscosity, melting point, and glass transition temperatures solely through physics-based models is challenging. Data-driven machine learning (ML) also poses challenges in constructing ML models, especially in the material science domain where data is limited. To address this, we integrate physics-informed descriptors from molecular dynamics (MD) simulations to enhance the accuracy and interpretability of ML models. Our current study focuses on accurately predicting viscosity in liquid systems using MD descriptors. In this work, we curated a comprehensive dataset of over 4000 small organic molecules' viscosities from scientific literature, publications, and online databases. This dataset enabled us to develop quantitative structure-property relationships (QSPR) consisting of descriptor-based and graph neural network models to predict temperature-dependent viscosities for a wide range of viscosities. The QSPR models reveal that including MD descriptors improves the prediction of experimental viscosities, particularly at the small data set scale of fewer than a thousand data points. Furthermore, feature importance tools reveal that intermolecular interactions captured by MD descriptors are most important for viscosity predictions. Finally, the QSPR models can accurately capture the inverse relationship between viscosity and temperature for six battery-relevant solvents, some of which were not included in the original data set. Our research highlights the effectiveness of incorporating MD descriptors into QSPR models, which leads to improved accuracy for properties that are difficult to predict when using physics-based models alone or when limited data is available.
Project description:Characterizing internal structures and defects in materials is a challenging task, often requiring solutions to inverse problems with unknown topology, geometry, material properties, and nonlinear deformation. Here, we present a general framework based on physics-informed neural networks for identifying unknown geometric and material parameters. By using a mesh-free method, we parameterize the geometry of the material using a differentiable and trainable method that can identify multiple structural features. We validate this approach for materials with internal voids/inclusions using constitutive models that encompass the spectrum of linear elasticity, hyperelasticity, and plasticity. We predict the size, shape, and location of the internal void/inclusion as well as the elastic modulus of the inclusion. Our general framework can be applied to other inverse problems in different applications that involve unknown material properties and highly deformable geometries, targeting material characterization, quality assurance, and structural design.
Project description:Fish detect predators, flow conditions, environments and each other through pressure signals. Lateral line ablation is often performed to understand the role of pressure sensing. In the present study, we propose a non-invasive method for reconstructing the instantaneous pressure field sensed by a fish's lateral line system from two-dimensional particle image velocimetry (PIV) measurements. The method uses a physics-informed neural network (PINN) to predict an optimized solution for the pressure field near and on the fish's body that satisfies both the Navier-Stokes equations and the constraints put forward by the PIV measurements. The method was validated using a direct numerical simulation of a swimming mackerel, Scomber scombrus, and was applied to experimental data of a turning zebrafish, Danio rerio. The results demonstrate that this method is relatively insensitive to the spatio-temporal resolution of the PIV measurements and accurately reconstructs the pressure on the fish's body.