CAREER: Uncertainty-Aware Thermodynamic Equations of State from Molecular Simulation and Experimental Data

Accurate predictions of thermodynamic properties such as density, solubility, and boiling point are important in science and engineering because they enable experts to understand how materials behave. The predictions are used in many areas ranging from designing chemical manufacturing processes to predicting how medicines move through the body. Engineers often rely on mathematical tools called equations of state (EoS) to make these predictions. However, building accurate EoS usually requires large amounts of data and advanced computing power. When only limited data are available, the EoS may not be accurate. This can lead to costly or dangerous mistakes, especially in industrial settings where safety is critical. This project will use modern machine learning methods to create better EoS that work well with limited data, to improve prediction accuracy, and to provide estimates of uncertainty. It will also support new chemical engineering courses focused on data science and include hands-on learning activities for K–12 students, helping to prepare a future STEM workforce and improving decision-making in areas like public health and industrial design. This project will use Gaussian Process Regression (GPR)to develop equations of state (EoS) that rigorously quantify predictive uncertainty. In GPR, each model prediction is represented as a Gaussian probability distribution, where the mean provides the predicted value and the standard deviation provides a corresponding uncertainty estimate. The primary focus will be on modeling thermodynamic free energies as functions of their natural variables, enabling the calculation of all derived thermodynamic properties through appropriate derivative relationships. The work will extend heteroscedastic GPR frameworks to EoS development by constructing covariance kernels capable of handling mixed derivative observations and by implementing training protocols that explicitly incorporate phase-equilibrium constraints. The fidelity of predicted uncertainties will be systematically evaluated to determine whether they (i) correlate with deviations from reference or ground-truth data, (ii) highlight regions where thermodynamic behavior inherently leads to increased uncertainty, and (iii) enable objective comparison and ranking of analytical EoS formulations. Additionally, uncertainty estimates will guide adaptive data acquisition strategies in molecular simulation and experimental design, reducing the cost and effort required for model development. Computational efficiency will be further enhanced through hierarchical or nested GPR structures that integrate multiple levels of analytical theory and data while retaining calibrated uncertainty quantification. The project will strengthen the integration of rigorous uncertainty quantification into thermodynamic modeling for science and engineering applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2543096 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Jacob Monroe | Institution: University of Arkansas, FAYETTEVILLE, AR | Award Amount: $563,155 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2543096 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2543096.html