Session: CIE-05-01CIE Graduate Student Poster Symposium

Paper Number: 74873

Start Time: August 18, 10:00 AM

74873 - Uncertainty Quantification With Label-Free Regression 

My research is uncertainty quantification (UQ) with label-free regression, and UQ is one of the areas in advanced modeling and simulation (AMS). If the physical model contains uncertainty in its input and parameters, its simulation results will also contain uncertainty. Since the model needs to be called repeatedly, the UQ task is computationally expensive. My focus is to alleviate the computational cost by building a surrogate for the model using label-free regression. Attending the conference will provide me with a good opportunity to present my work and obtain professional feedback. 

Overview

My research focus is uncertainty quantification with nonlinear partial differential equations and physics-informed machine learning. With high-dimensional input and output data, solving partial differential equations (PDEs) is expensive, especially for uncertainty quantification (UQ). My objective is to create surrogate models to replace expensive PDEs for UQ. I am currently working on label-free regression that will not solve PDEs but only evaluate PDEs. This method can save computational time significantly.

Motivation and State of the Art

Engineering design increasingly relies on numerical simulation, and simulation models also rely on input data. The input variables (data) are typically uncertain due to the random nature of the problem. Numerical simulation relies on input data and constraints to build complex physical or engineering systems, the model is built by approximating the input-output relation in a system. However, the input data requires uncertainty quantification due to the simulation data being randomly generated.

In most cases, it is very difficult to obtain complete information (or in the absence of label data) to build a model. Meanwhile, calling simulation models is time-consuming. Label free is a good method to reduce computational cost, it is used in supervising neural networks by specifying the relations (constraints) between the input space and output space. Partial differential equations combined with label-free and uncertainty quantification can be used as function approximators that can encode any underlying physical laws that govern a given dataset.

The process of uncertainty quantification requires repeated calling of simulation models; therefore, it is extremely computationally expensive. The regression model has been used to effectively reduce the computational cost. The reason why I am applying label-free method into uncertainty quantification is that this method is successful in saving simulation time but has not been widely used for uncertainty quantification. My motivation is to combine them into one method to build a model effectively.

With the explosive growth of computing resources, there have been fundamental improvements in machine learning and label-free data analysis. Data-fit surrogates have been used for a wide range of uncertainty quantification problems. Data-driven solutions (Raissi, Perdikaris, et al. 2017) provide a good method that uses neural-network and any given constraints of physics to solve the partial differential equations. However, traditional data-fit models have a hard time handling the problems with strong nonlinearities equations or high dimensional input data.

Presenting Author: Huiru li purdue university

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