Thomas Edison synthesized around 6000 materials in the laboratory to discover the appropriate material for the filament of incandescent light bulbs. However, these days researchers synthesize materials on a computer, and use mathematical models to study their properties. This saves time and money.

In order to synthesize a material on a computer, researchers need to know the atomic configuration of the material (for example, see Fig. 1). The atomic configuration is the one that corresponds to minimum potential energy. In this project, our objective is to:

1. Develop a methodology to adaptively select a subset of atomic configurations that represent all the possible configurations.

2. Perform Bayesian optimization on the representative set of configurations to find the one with minimum potential energy.

Key contributions of the developed methodology:

1. Using our methodology, we are able to explore a larger domain space of all possible configurations with much lesser number of points (Fig. 2), as compared to the traditional method of random sampling.

2. Using the Bayesian optimization approach, we are able to find the configuration with the minimum energy in very few iterations, as compared to the traditional approach of using local gradient descent at a number of randomly selected points.

This will let the material scientists find the global minimum much more quickly and efficiently than the current procedures. A paper on the entire method of obtaining the global minimum is submitted.

Independently modulating the phase and amplitude of an acoustic wave has critical applications such as non-invasive surgery. In this work, we develop a methodology to obtain a design that provides the desired phase and amplitude of the reflected and transmitted waves. A manuscript on this work can be found here.

Industries often generate data using mathematical models to understand a physical process. These models mimic the physical process under study. However, such models may contain unknown parameters or may have some discrepancy with reality. Thus, industries perform physical experiments to calibrate such models so that they accurately mimic the physical process (Fig. 4). However, physical experiments are usually expensive, and thus need to be carefully designed to efficiently calibrate the model, i.e., calibrate with a few design points. I collaborated with the Procter & Gamble company to develop a methodology that addresses the issue of designing such a physical experiment. We propose an experimental design that is a combination of two designs. Some points in the design are optimal for estimating the unknown calibration parameters, while other points are optimal for estimating the potential model discrepancy. Thus, the novelty of our proposed design is that it is optimal for estimating the unknown parameters, while simultaneously also being robust to potential discrepancy in the mathematical model. We applied our design methodology to calibrate a physics-based model used at P&G. We found that the calibrated model obtained using our design resembles reality more closely than those obtained using traditional designs. Engineers are usually unaware of the presence or absence of discrepancy in the mathematical model. This research provides them with a solution that works reasonably well in both cases – the presence or absence of discrepancy. The manuscript of this work can be found here.