Quantifying uncertainty in the response quantity is a big issue for small and large-scale problems. For small-scale nonlinear problems (e.g. impact oscillator with a few uncertain parameters), it is important to understand the behavior of the stochastic responses by accurately quantifying the uncertainty. On the other hand, handling a large number of uncertain parameters and accurately quantifying uncertainty for the responses are challenging tasks for large-scale problems.

For the prediction of stochastic response quantity, a bridging paradigm is needed, which is called a surrogate model or, meta-model. We develop different kinds of surrogate models to predict the stochastic response behavior of an uncertain problem. We develop surrogate models for uncertain static and dynamic problems.

Most of the surrogate models are data-driven and we often don't account for the data that represent the physics of a system. With the physics-informed approach, the physical behavior of a system can be modeled more accurately. We use conservation of energy or conservation of momentum theory for formulating a physics-based machine learning approach. Physics-informed machine learning can be applied for solving a variety of problems ranging from mechanics to dynamics.

Reliability analysis is performed to predict the failure probability of an element or a structure considering a threshold value for a response quantity. It can be done at the element level or at the system level depending on the requirement. We develop different approaches to predict the failure probability accurately and efficiently.

Global sensitivity analysis identifies the importance of the input uncertain parameters on the uncertain output quantities. We develop different approaches for predicting the global sensitivity accurately for static as well as the dynamical systems. We also quantify the sensitivity of the input parameters on the failure probability of a system.