Search Results for author:
Found 105 papers, 34 papers with code
Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks
Additionally, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels.
DeepVIVONet: Using deep neural operators to optimize sensor locations with application to vortex-induced vibrations
We introduce DeepVIVONet, a new framework for optimal dynamic reconstruction and forecasting of the vortex-induced vibrations (VIV) of a marine riser, using field data.
Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach
We formulate reconstruction as a mapping from incomplete observed data to full reconstructed fields.
KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a new two-block architecture that combines robust multi-layer perceptron (MLP) based inner functions with flexible linear combinations of basis functions as outer functions.
A Digital twin for Diesel Engines: Operator-infused PINNs with Transfer Learning for Engine Health Monitoring
The objective of this study is to develop a computationally efficient neural network-based approach for identifying unknown parameters of a mean value diesel engine model to facilitate physics-based health monitoring and maintenance forecasting.
Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures
Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on ad-hoc assumptions.
Randomized Forward Mode Gradient for Spiking Neural Networks in Scientific Machine Learning
Spiking neural networks (SNNs) represent a promising approach in machine learning, combining the hierarchical learning capabilities of deep neural networks with the energy efficiency of spike-based computations.
From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements.
HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models
The interplay between stochastic processes and optimal control has been extensively explored in the literature.
Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling
We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows.
State-space models are accurate and efficient neural operators for dynamical systems
We demonstrate Mamba's superior performance in both interpolation and challenging extrapolation tasks.
Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations
We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs).
SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification
Herein, we introduce Symplectic Graph Neural Networks (SympGNNs) that can effectively handle system identification in high-dimensional Hamiltonian systems, as well as node classification.
Physics-Informed Neural Networks and Extensions
In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery of governing differential equations.
Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology
With a specific focus on biological and physiological models, this study investigates the decomposition of total uncertainty in the estimation of states and parameters of a differential system simulated with MC X-TFC, a new physics-informed approach for uncertainty quantification based on random projections and Monte-Carlo sampling.
Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving
Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries.
NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements
This study introduces NeuroSEM, a hybrid framework integrating PINNs with the high-fidelity Spectral Element Method (SEM) solver, Nektar++.
Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks
This physics-informed machine learning method enables us to infer continuous temperature fields using only sparse velocity data, hence eliminating the need for direct temperature measurements.
Kolmogorov-Arnold Networks
Physics-informed machine learning
Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations
We introduce an innovative approach for solving high-dimensional Fokker-Planck-L\'evy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance, and ecology.
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks
We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100, 000 dimensions.
Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications
We introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications.
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative representation model to MLP.
Kolmogorov-Arnold Networks
Physics-informed machine learning
Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity
Transformers have not been used in that capacity, and specifically, they have not been tested for solutions of PDEs with low regularity.
Large scale scattering using fast solvers based on neural operators
We extend a recently proposed machine-learning-based iterative solver, i. e. the hybrid iterative transferable solver (HINTS), to solve the scattering problem described by the Helmholtz equation in an exterior domain with a complex absorbing boundary condition.
GMC-PINNs: A new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains
Our results demonstrate the effectiveness of GMC-PINNs in dealing with irregular domain problems and show a higher computational efficiency compared to the original fPINN method.
Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning
We provide several examples from SciML involving noisy data and \textit{epistemic uncertainty} to illustrate the potential advantages of our approach.
Learning in PINNs: Phase transition, total diffusion, and generalization
We investigate the learning dynamics of fully-connected neural networks through the lens of gradient signal-to-noise ratio (SNR), examining the behavior of first-order optimizers like Adam in non-convex objectives.
Two-scale Neural Networks for Partial Differential Equations with Small Parameters
We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs).
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling.
RiemannONets: Interpretable Neural Operators for Riemann Problems
Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis.
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks
We further showcase HTE's convergence to the original PINN loss and its unbiased behavior under specific conditions.
AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression
The performance of this framework is validated by recovering the right-hand sides and unknown terms of certain complex, chaotic systems such as the well-known Lorenz system, a six-dimensional hyperchaotic system, and the non-autonomous Sprott chaotic system, and comparing them with their known analytical expressions.
Rethinking materials simulations: Blending direct numerical simulations with neural operators
This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism that enables accurate extrapolation and efficient time-to-solution predictions of the dynamics.
GPT vs Human for Scientific Reviews: A Dual Source Review on Applications of ChatGPT in Science
Herein, we consider 13 GPT-related papers across different scientific domains, reviewed by a human reviewer and SciSpace, a large language model, with the reviews evaluated by three distinct types of evaluators, namely GPT-3. 5, a crowd panel, and GPT-4.
Rethinking Skip Connections in Spiking Neural Networks with Time-To-First-Spike Coding
In this work, we delve into the role of skip connections, a widely used concept in Artificial Neural Networks (ANNs), within the domain of SNNs with TTFS coding.
Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs
To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version.
Mechanical Characterization and Inverse Design of Stochastic Architected Metamaterials Using Neural Operators
Our work marks a significant advancement in the field of materials-by-design, potentially heralding a new era in the discovery and development of next-generation metamaterials with unparalleled mechanical characteristics derived directly from experimental insights.
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators
As a result, UQ for noisy inputs becomes a crucial factor for reliable and trustworthy deployment of these models in applications involving physical knowledge.
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning
This connection allows us to reinterpret incremental updates to learned models as the evolution of an associated HJ PDE and optimal control problem in time, where all of the previous information is intrinsically encoded in the solution to the HJ PDE.
Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions
Initially, we utilize DeepONet to learn the solution operator for a set of smooth problems relevant to the PDEs characterized by sharp solutions.
Correcting model misspecification in physics-informed neural networks (PINNs)
Despite the effectiveness of PINNs for discovering governing equations, the physical models encoded in PINNs may be misspecified in complex systems as some of the physical processes may not be fully understood, leading to the poor accuracy of PINN predictions.
Learning characteristic parameters and dynamics of centrifugal pumps under multiphase flow using physics-informed neural networks
Electrical submersible pumps (ESPs) are prevalently utilized as artificial lift systems in the oil and gas industry.
DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networks
Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data.
AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification
The proposed framework -- named AI-Aristotle -- combines eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification.
Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning
We introduce a method to convert Physics-Informed Neural Networks (PINNs), commonly used in scientific machine learning, to Spiking Neural Networks (SNNs), which are expected to have higher energy efficiency compared to traditional Artificial Neural Networks (ANNs).
Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators
We address the challenge of sound propagation simulations in 3D virtual rooms with moving sources, which have applications in virtual/augmented reality, game audio, and spatial computing.
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks
We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach.
Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs
Subsequently, the closed form dependency of parameter values found by PINN on the initial radii and contact angles are given using symbolic regression.
Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO)
The proposed method, named Diffusion-inspired Temporal Transformer Operator (DiTTO), is inspired by latent diffusion models and their conditioning mechanism, which we use to incorporate the temporal evolution of the PDE, in combination with elements from the transformer architecture to improve its capabilities.
Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression
Specifically, we integrate physics informed neural networks (PINNs) and symbolic regression to discover a reaction-diffusion type partial differential equation for tau protein misfolding and spreading.
TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers
Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics.
Residual-based attention and connection to information bottleneck theory in PINNs
Driven by the need for more efficient and seamless integration of physical models and data, physics-informed neural networks (PINNs) have seen a surge of interest in recent years.
Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies
We propose to enhance the training of physics-informed neural networks (PINNs).
MyCrunchGPT: A chatGPT assisted framework for scientific machine learning
To demonstrate the flow of the MyCrunchGPT, and create an infrastructure that can facilitate a broader vision, we built a webapp based guided user interface, that includes options for a comprehensive summary report.
A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data
In addition, symbolic regression is employed to determine the closed form of the unknown part of the equation from the data, and the results confirm the accuracy of the X-PINNs based approach.
A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes
Quantifying biomechanical properties of the human vasculature could deepen our understanding of cardiovascular diseases.
Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel engines
In other words, the mean value model uses both the PINN model and the DNNs to represent the engine's states, with the PINN providing a physics-based understanding of the engine's overall dynamics and the DNNs offering a more engine-specific and adaptive representation of the empirical formulae.
Learning in latent spaces improves the predictive accuracy of deep neural operators
Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems.
Real-Time Prediction of Gas Flow Dynamics in Diesel Engines using a Deep Neural Operator Framework
As an alternative to physics based models, we develop an operator-based regression model (DeepONet) to learn the relevant output states for a mean-value gas flow engine model using the engine operating conditions as input variables.
Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences.
LNO: Laplace Neural Operator for Solving Differential Equations
Herein, we demonstrate the superior approximation accuracy of a single Laplace layer in LNO over four Fourier modules in FNO in approximating the solutions of three ODEs (Duffing oscillator, driven gravity pendulum, and Lorenz system) and three PDEs (Euler-Bernoulli beam, diffusion equation, and reaction-diffusion system).
ViTO: Vision Transformer-Operator
We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs).
Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks
Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly from observational data.
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions
This problem is also found in, and in some sense more difficult, with domain decomposition strategies such as temporal decomposition using XPINNs.
Learning stiff chemical kinetics using extended deep neural operators
Specifically, to train the DeepONet for the syngas model, we solve the skeletal kinetic model for different initial conditions.
Learning bias corrections for climate models using deep neural operators
In this study, we replace the bias correction process with a surrogate model based on the Deep Operator Network (DeepONet).
Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils
Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications.
A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modeling
One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise.
L-HYDRA: Multi-Head Physics-Informed Neural Networks
We introduce multi-head neural networks (MH-NNs) to physics-informed machine learning, which is a type of neural networks (NNs) with all nonlinear hidden layers as the body and multiple linear output layers as multi-head.
Reliable extrapolation of deep neural operators informed by physics or sparse observations
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks.
SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations
We propose a Spiking Neural Network (SNN)-based explicit numerical scheme for long time integration of time-dependent Ordinary and Partial Differential Equations (ODEs, PDEs).
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology
We also show cases where XPINN is already better than PINN, so APINN can still slightly improve XPINN.
How important are activation functions in regression and classification? A survey, performance comparison, and future directions
For this purpose, we also discuss various requirements for activation functions that have been used in the physics-informed machine learning framework.
Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers
Neural networks suffer from spectral bias having difficulty in representing the high frequency components of a function while relaxation methods can resolve high frequencies efficiently but stall at moderate to low frequencies.
NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators
In this paper, we present an open-source Python library (https://github. com/Crunch-UQ4MI), termed NeuralUQ and accompanied by an educational tutorial, for employing UQ methods for SciML in a convenient and structured manner.
G2Φnet: Relating Genotype and Biomechanical Phenotype of Tissues with Deep Learning
Many genetic mutations adversely affect the structure and function of load-bearing soft tissues, with clinical sequelae often responsible for disability or death.
Physics-Informed Deep Neural Operator Networks
Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e. g., in an advection-diffusion-reaction partial differential equation, or simply as a black box, e. g., a system-of-systems.
Spiking Neural Operators for Scientific Machine Learning
We demonstrate this new approach for classification using the SNN in the branch, achieving results comparable to the literature.
Scalable algorithms for physics-informed neural and graph networks
For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs).
BIG-bench Machine Learning
Physics-informed machine learning
Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems
Our study reveals the inherent advantages and disadvantages of Neural Networks, Bayesian Inference, and a combination of both and provides valuable guidelines for model selection.
Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms
Thoracic aortic aneurysm (TAA) is a localized dilatation of the aorta resulting from compromised wall composition, structure, and function, which can lead to life-threatening dissection or rupture.
Deep transfer operator learning for partial differential equations under conditional shift
Transfer learning (TL) enables the transfer of knowledge gained in learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labeling, potential computational power limitations, and dataset distribution mismatches.
Learning two-phase microstructure evolution using neural operators and autoencoder architectures
We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space.
Discovering and forecasting extreme events via active learning in neural operators
This model-agnostic framework pairs a BED scheme that actively selects data for quantifying extreme events with an ensemble of DNOs that approximate infinite-dimensional nonlinear operators.
On the influence of over-parameterization in manifold based surrogates and deep neural operators
In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics.
Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems
In this work, we explore the idea of multiscale modeling with machine learning and employ DeepONet, a neural operator, as an efficient surrogate of the expensive solver.
Physics-informed neural networks for inverse problems in supersonic flows
Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles.
Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks
The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements.
Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods.
SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems
Solving high-dimensional optimal control problems in real-time is an important but challenging problem, with applications to multi-agent path planning problems, which have drawn increased attention given the growing popularity of drones in recent years.
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
We tested gPINNs extensively and demonstrated the effectiveness of gPINNs in both forward and inverse PDE problems.
DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs
However, recent advances mostly focus on learning node embeddings as deterministic "vectors" for static graphs yet disregarding the key graph temporal dynamics and the evolving uncertainties associated with node embedding in the latent space.
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
Specifically, for general multi-layer PINNs and XPINNs, we first provide a prior generalization bound via the complexity of the target functions in the PDE problem, and a posterior generalization bound via the posterior matrix norms of the networks after optimization.
GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems
We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism.
Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network
Aortic dissection progresses via delamination of the medial layer of the wall.
Meta-learning PINN loss functions
In the computational examples, the meta-learned losses are employed at test time for addressing regression and PDE task distributions.
Learning Functional Priors and Posteriors from Data and Physics
In summary, the proposed method is capable of learning flexible functional priors, and can be extended to big data problems using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.
AOSLO-net: A deep learning-based method for automatic segmentation of retinal microaneurysms from adaptive optics scanning laser ophthalmoscope images
Microaneurysms (MAs) are one of the earliest signs of diabetic retinopathy (DR), a frequent complication of diabetes that can lead to visual impairment and blindness.
Physics-informed neural networks (PINNs) for fluid mechanics: A review
Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE.
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions
We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions.
A Caputo fractional derivative-based algorithm for optimization
We propose three versions -- non-adaptive, adaptive terminal and adaptive order.
Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates
We propose a simple but effective modification of the discriminators, namely measure-conditional discriminators, as a plug-and-play module for different GANs.
Operator learning for predicting multiscale bubble growth dynamics
Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs).
Computational Physics
Multi-fidelity Bayesian Neural Networks: Algorithms and Applications
We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs).
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data.
