Faaiq Waqar

Faaiq G. Waqar, Swati Patel, Cory M. Simon

Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of the system, reconstruct the input to it that caused some observed output. Applied inverse problems are challenging because a solution may (i) not exist, (ii) not be unique, or (iii) be sensitive to measurement noise contaminating the data. Bayesian statistical inversion (BSI) is an approach to tackle ill-posed and/or ill-conditioned inverse problems. Advantageously, BSI provides a "solution" that (i) quantifies uncertainty by assigning a probability to each possible value of the unknown parameter/input and (ii) incorporates prior information and beliefs about the parameter/input. Herein, we provide a tutorial of BSI for inverse problems, by way of illustrative examples dealing with heat transfer from ambient air to a cold lime fruit. First, we use BSI to infer a parameter in a dynamic model of the lime temperature from measurements of the lime temperature over time. Second, we use BSI to reconstruct the initial condition of the lime from a measurement of its temperature later in time. We demonstrate the incorporation of prior information, visualize the posterior distributions of the parameter/initial condition, and show posterior samples of lime temperature trajectories from the model. Our tutorial aims to reach a wide range of scientists and engineers.

Ali Raza, Faaiq Waqar, Arni Sturluson et al.

Metal-organic framework (MOFs) are nanoporous materials that could be used to capture carbon dioxide from the exhaust gas of fossil fuel power plants to mitigate climate change. In this work, we design and train a message passing neural network (MPNN) to predict simulated CO$_2$ adsorption in MOFs. Towards providing insights into what substructures of the MOFs are important for the prediction, we introduce a soft attention mechanism into the readout function that quantifies the contributions of the node representations towards the graph representations. We investigate different mechanisms for sparse attention to ensure only the most relevant substructures are identified.