A novel data generation scheme for surrogate modelling with deep
operator networks
- URL: http://arxiv.org/abs/2402.16903v1
- Date: Sat, 24 Feb 2024 14:42:42 GMT
- Title: A novel data generation scheme for surrogate modelling with deep
operator networks
- Authors: Shivam Choubey, Birupaksha Pal, Manish Agrawal
- Abstract summary: We propose a novel methodology to alleviate the computational burden associated with training data generation for DeepONets.
Unlike existing literature, the proposed framework for data generation does not use any partial differential equation integration strategy.
The proposed methodology can be extended to other operator learning methods, making the approach widely applicable.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Operator-based neural network architectures such as DeepONets have emerged as
a promising tool for the surrogate modeling of physical systems. In general,
towards operator surrogate modeling, the training data is generated by solving
the PDEs using techniques such as Finite Element Method (FEM). The
computationally intensive nature of data generation is one of the biggest
bottleneck in deploying these surrogate models for practical applications. In
this study, we propose a novel methodology to alleviate the computational
burden associated with training data generation for DeepONets. Unlike existing
literature, the proposed framework for data generation does not use any partial
differential equation integration strategy, thereby significantly reducing the
computational cost associated with generating training dataset for DeepONet. In
the proposed strategy, first, the output field is generated randomly,
satisfying the boundary conditions using Gaussian Process Regression (GPR).
From the output field, the input source field can be calculated easily using
finite difference techniques. The proposed methodology can be extended to other
operator learning methods, making the approach widely applicable. To validate
the proposed approach, we employ the heat equations as the model problem and
develop the surrogate model for numerous boundary value problems.
Related papers
- Scaling up Probabilistic PDE Simulators with Structured Volumetric Information [23.654711580674885]
We propose a framework combining a discretization scheme based on the popular Finite Volume Method with complementary numerical linear algebra techniques.
Experiments, including atemporal tsunami simulation, demonstrate substantially improved scaling behavior of this approach over previous collocation-based techniques.
arXiv Detail & Related papers (2024-06-07T15:38:27Z) - Deep Learning-based surrogate models for parametrized PDEs: handling
geometric variability through graph neural networks [0.0]
This work explores the potential usage of graph neural networks (GNNs) for the simulation of time-dependent PDEs.
We propose a systematic strategy to build surrogate models based on a data-driven time-stepping scheme.
We show that GNNs can provide a valid alternative to traditional surrogate models in terms of computational efficiency and generalization to new scenarios.
arXiv Detail & Related papers (2023-08-03T08:14:28Z) - Training Deep Surrogate Models with Large Scale Online Learning [48.7576911714538]
Deep learning algorithms have emerged as a viable alternative for obtaining fast solutions for PDEs.
Models are usually trained on synthetic data generated by solvers, stored on disk and read back for training.
It proposes an open source online training framework for deep surrogate models.
arXiv Detail & Related papers (2023-06-28T12:02:27Z) - Data efficient surrogate modeling for engineering design: Ensemble-free
batch mode deep active learning for regression [0.6021787236982659]
We propose a simple and scalable approach for active learning that works in a student-teacher manner to train a surrogate model.
By using this proposed approach, we are able to achieve the same level of surrogate accuracy as the other baselines like DBAL and Monte Carlo sampling.
arXiv Detail & Related papers (2022-11-16T02:31:57Z) - Exploiting Temporal Structures of Cyclostationary Signals for
Data-Driven Single-Channel Source Separation [98.95383921866096]
We study the problem of single-channel source separation (SCSS)
We focus on cyclostationary signals, which are particularly suitable in a variety of application domains.
We propose a deep learning approach using a U-Net architecture, which is competitive with the minimum MSE estimator.
arXiv Detail & Related papers (2022-08-22T14:04:56Z) - Deep Variational Models for Collaborative Filtering-based Recommender
Systems [63.995130144110156]
Deep learning provides accurate collaborative filtering models to improve recommender system results.
Our proposed models apply the variational concept to injectity in the latent space of the deep architecture.
Results show the superiority of the proposed approach in scenarios where the variational enrichment exceeds the injected noise effect.
arXiv Detail & Related papers (2021-07-27T08:59:39Z) - Conservative Objective Models for Effective Offline Model-Based
Optimization [78.19085445065845]
Computational design problems arise in a number of settings, from synthetic biology to computer architectures.
We propose a method that learns a model of the objective function that lower bounds the actual value of the ground-truth objective on out-of-distribution inputs.
COMs are simple to implement and outperform a number of existing methods on a wide range of MBO problems.
arXiv Detail & Related papers (2021-07-14T17:55:28Z) - Local approximate Gaussian process regression for data-driven
constitutive laws: Development and comparison with neural networks [0.0]
We show how to use local approximate process regression to predict stress outputs at particular strain space locations.
A modified Newton-Raphson approach is proposed to accommodate for the local nature of the laGPR approximation when solving the global structural problem in a FE setting.
arXiv Detail & Related papers (2021-05-07T14:49:28Z) - Offline Model-Based Optimization via Normalized Maximum Likelihood
Estimation [101.22379613810881]
We consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points.
This problem setting emerges in many domains where function evaluation is a complex and expensive process.
We propose a tractable approximation that allows us to scale our method to high-capacity neural network models.
arXiv Detail & Related papers (2021-02-16T06:04:27Z) - Model-Based Deep Learning [155.063817656602]
Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques.
Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance.
We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
arXiv Detail & Related papers (2020-12-15T16:29:49Z) - Variational Model-based Policy Optimization [34.80171122943031]
Model-based reinforcement learning (RL) algorithms allow us to combine model-generated data with those collected from interaction with the real system in order to alleviate the data efficiency problem in RL.
We propose an objective function as a variational lower-bound of a log-likelihood of a log-likelihood to jointly learn and improve model and policy.
Our experiments on a number of continuous control tasks show that despite being more complex, our model-based (E-step) algorithm, called emactoral model-based policy optimization (VMBPO), is more sample-efficient and
arXiv Detail & Related papers (2020-06-09T18:30:15Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.