Estimating Material Parameters for a One-Dimensional Heat Equation with a Physics-Informed Neural Network
Source abstract
Abstract
A physics-informed neural network (PINN) is developed to estimate the spatially varying parameters of the time-dependent heat equation in one dimension. The proposed model incorporates both the forward and inverse problems to estimate the temperature and thermal properties of a laser-induced interaction with biological tissue. The network can detect the presence and location of a second layer of tissue, if it exists, and estimate the thermal coefficients of each substance. This ability to model nonhomogeneous properties in tissue subjected to laser irradiation has many important applications in medical procedures. An ensemble method is used to quantify the epistemic uncertainty of all estimates to identify weaknesses in the model. Aleotoric uncertainty is simulated through noise perturbations, demonstrating robust estimates in the presence of measurement error. The uncertainty associated with parameter estimation provides insight into the ill-posedness of the inverse problem.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Numerical methods in inverse problems · Model Reduction and Neural Networks · Thermoelastic and Magnetoelastic Phenomena
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
711th Human Performance Wing, Human Effectiveness Directorate, Bioeffects Division JBSA, Fort Sam Houston, TX 78234, USA
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Center for Trustworthy Artificial Intelligence Through Model Risk Management (TAIMing AI), University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Funding
National Academies of Sciences, Engineering, and Medicine
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