Search Results for author:
Found 56 papers, 17 papers with code
Self-Modulating Nonparametric Event-Tensor Factorization
Tensor factorization is a fundamental framework to analyze high-order interactions in data.
Spatio-temporal Fourier Transformer (StFT) for Long-term Dynamics Prediction
Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering.
Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Data
Neural operators have shown great potential in surrogate modeling.
Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation
ACMFD can perform a wide range of tasks within a single framework, including forward prediction, various inverse problems, and simulating data for entire systems or subsets of quantities conditioned on others.
Toward Efficient Kernel-Based Solvers for Nonlinear PDEs
In numerical experiments, we demonstrate the advantages of our method in solving several benchmark PDEs.
Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases
We find that strong BC PINNs can better learn the amplitudes of high-frequency components of the target solutions.
HyResPINNs: Adaptive Hybrid Residual Networks for Learning Optimal Combinations of Neural and RBF Components for Physics-Informed Modeling
We present a new class of PINNs called HyResPINNs, which augment traditional PINNs with adaptive hybrid residual blocks that combine the outputs of a standard neural network and a radial basis function (RBF) network.
Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning
This paper introduces the Kernel Neural Operator (KNO), a novel operator learning technique that uses deep kernel-based integral operators in conjunction with quadrature for function-space approximation of operators (maps from functions to functions).
Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients
This paper proposes a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery.
Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
We present polynomial-augmented neural networks (PANNs), a novel machine learning architecture that combines deep neural networks (DNNs) with a polynomial approximant.
ElastoGen: 4D Generative Elastodynamics
We present ElastoGen, a knowledge-driven AI model that generates physically accurate 4D elastodynamics.
Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems
In this paper, we propose an invertible Fourier Neural Operator (iFNO) that tackles both the forward and inverse problems.
Standard Gaussian Process Can Be Excellent for High-Dimensional Bayesian Optimization
Second, our theoretical analysis reveals that the SE kernels failure primarily stems from improper initialization of the length-scale parameters, which are commonly used in practice but can cause gradient vanishing in training.
Diffusion-Generative Multi-Fidelity Learning for Physical Simulation
We propose a conditional score model to control the solution generation by the input parameters and the fidelity.
Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data
To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT).
Solving High Frequency and Multi-Scale PDEs with Gaussian Processes
Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs).
Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels
To overcome the computational challenge of kernel regression, we place the function values on a mesh and induce a Kronecker product construction, and we use tensor algebra to enable efficient computation and optimization.
Multi-Resolution Active Learning of Fourier Neural Operators
To overcome this problem, we propose Multi-Resolution Active learning of FNO (MRA-FNO), which can dynamically select the input functions and resolutions to lower the data cost as much as possible while optimizing the learning efficiency.
BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition
More importantly, almost all methods assume the observations are sampled at regular time stamps, and fail to handle complex irregular sampled time series arising from different applications.
Provably Convergent Schrödinger Bridge with Applications to Probabilistic Time Series Imputation
We show that optimizing the transport cost improves the performance and the proposed algorithm achieves the state-of-the-art result in healthcare and environmental data while exhibiting the advantage of exploring both temporal and feature patterns in probabilistic time series imputation.
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.
Genetic Programming Based Symbolic Regression for Analytical Solutions to Differential Equations
In this paper, we present a machine learning method for the discovery of analytic solutions to differential equations.
Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions
One surprising trait of neural networks is the extent to which their connections can be pruned with little to no effect on accuracy.
Batch Multi-Fidelity Active Learning with Budget Constraints
However, this method only queries at one pair of fidelity and input at a time, and hence has a risk to bring in strongly correlated examples to reduce the learning efficiency.
Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks
However, the performance of multi-domain PINNs is sensitive to the choice of the interface conditions.
A Kernel Approach for PDE Discovery and Operator Learning
This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods.
Nonparametric Embeddings of Sparse High-Order Interaction Events
High-order interaction events are common in real-world applications.
Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition
In practice, tensor data is often accompanied by temporal information, namely the time points when the entry values were generated.
Infinite-Fidelity Coregionalization for Physical Simulation
Our model can interpolate and/or extrapolate the predictions to novel fidelities, which can be even higher than the fidelities of training data.
Recall Distortion in Neural Network Pruning and the Undecayed Pruning Algorithm
In this work, we study such relative distortions in recall by hypothesizing an intensification effect that is inherent to the model.
The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networks
We propose a tractable heuristic for solving the combinatorial extension of OBS, in which we select weights for simultaneous removal, as well as a systematic update of the remaining weights.
AutoIP: A United Framework to Integrate Physics into Gaussian Processes
Physical modeling is critical for many modern science and engineering applications.
Self-Adaptable Point Processes with Nonparametric Time Decays
Specifically, we use an embedding to represent each event type and model the event influence as an unknown function of the embeddings and time span.
A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs
Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world.
BIG-bench Machine Learning
Physics-informed machine learning
+1
Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes
Compared with the existent works, our model not only leverages the structural information underlying the observed entry indices, but also provides extra interpretability and flexibility -- it can simultaneously estimate a set of location factors about the intrinsic properties of the tensor nodes, and another set of sociability factors reflecting their extrovert activity in interacting with others; users are free to choose a trade-off between the two types of factors.
Meta-Learning with Adjoint Methods
the initialization, we only need to run the standard ODE solver twice -- one is forward in time that evolves a long trajectory of gradient flow for the sampled task; the other is backward and solves the adjoint ODE.
Characterizing possible failure modes in physics-informed neural networks
We provide evidence that the soft regularization in PINNs, which involves PDE-based differential operators, can introduce a number of subtle problems, including making the problem more ill-conditioned.
Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)
Candidates for this approach are simulation methodologies for which there are fidelity differences connected with significant computational cost differences.
Batch Multi-Fidelity Bayesian Optimization with Deep Auto-Regressive Networks
Bayesian optimization (BO) is a powerful approach for optimizing black-box, expensive-to-evaluate functions.
Deep Multi-Fidelity Active Learning of High-dimensional Outputs
The training examples can be collected with different fidelities to allow a cost/accuracy trade-off.
Block-term Tensor Neural Networks
Deep neural networks (DNNs) have achieved outstanding performance in a wide range of applications, e. g., image classification, natural language processing, etc.
Streaming Probabilistic Deep Tensor Factorization
Our algorithm provides responsive incremental updates for the posterior of the latent factors and NN weights upon receiving new tensor entries, and meanwhile select and inhibit redundant/useless weights.
Multi-Fidelity Bayesian Optimization via Deep Neural Networks
In many applications, the objective function can be evaluated at multiple fidelities to enable a trade-off between the cost and accuracy.
Physics Informed Deep Kernel Learning
Deep kernel learning is a promising combination of deep neural networks and nonparametric function learning.
Multi-Fidelity High-Order Gaussian Processes for Physical Simulation
To address these issues, we propose Multi-Fidelity High-Order Gaussian Process (MFHoGP) that can capture complex correlations both between the outputs and between the fidelities to enhance solution estimation, and scale to large numbers of outputs.
Scalable Variational Gaussian Process Regression Networks
Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable.
Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications
To address this issue, this study presents a new modeling framework, named physics regularized machine learning (PRML), to encode classical traffic flow models (referred as physical models) into the ML architecture and to regularize the ML training process.
Probabilistic Streaming Tensor Decomposition with Side Information
Tensor decomposition is an essential tool to analyze high-order interactions in multiway data.
Conditional Expectation Propagation
Expectation propagation (EP) is a powerful approximate inference algorithm.
Probabilistic Streaming Tensor Decomposition
Tensor decomposition is a fundamental tool for multiway data analysis.
Stochastic Nonparametric Event-Tensor Decomposition
Tensor decompositions are fundamental tools for multiway data analysis.
Learning Compact Recurrent Neural Networks with Block-Term Tensor Decomposition
On three challenging tasks, including Action Recognition in Videos, Image Captioning and Image Generation, BT-RNN outperforms TT-RNN and the standard RNN in terms of both prediction accuracy and convergence rate.
Asynchronous Distributed Variational Gaussian Processes for Regression
Gaussian processes (GPs) are powerful non-parametric function estimators.
Distributed Flexible Nonlinear Tensor Factorization
Tensor factorization is a powerful tool to analyse multi-way data.
DinTucker: Scaling up Gaussian process models on multidimensional arrays with billions of elements
To overcome this limitation, we present Distributed Infinite Tucker (DINTUCKER), a large-scale nonlinear tensor decomposition algorithm on MAPREDUCE.
Supervised Heterogeneous Multiview Learning for Joint Association Study and Disease Diagnosis
To unify these two tasks, we present a new sparse Bayesian approach for joint association study and disease diagnosis.
