Research theme four of five
Inverse problems and probabilistic inference
What can an aggregate measurement tell you about the hidden mechanical cause that produced it, and when is the honest answer that several causes are equally consistent with the data?
The problem
Identification in structural dynamics is usually posed as an optimisation: find the parameters that best reproduce the measurement. That formulation hides the question that matters, which is whether the measurement determines the parameters at all. Damping is the clearest case. A measured frequency response can be reproduced by a viscous model, a non-viscous model with a suitable kernel, or by an ensemble of undamped systems with dispersed frequencies, and the three carry entirely different predictions for anything else.
The programme here is to treat identification as inference, with an explicit account of how far the data constrain the answer.
Why it matters
An updated model that reproduces the measurements is useful only once you know how far the measurements pin it down. Several very different parameter sets can fit the same frequency response to within test scatter, and choosing one of them by optimisation hides that fact behind a single answer. Stating the identifiable subspace instead gives an engineer something a certification argument can use: this quantity is determined by the data, this one is assumed, and here is the interval. The same statement is what makes a digital twin honest about the limits of its own confidence, and it is what turns a nanoscale resonator into a mass sensor with a stated resolution.
Current frontier
- identifiability and non-uniqueness in dynamic inverse problems
- probabilistic attribution: dissipation against dispersion
- inverse spectral problems and disorder identification
- Bayesian and simulation-based inference
- stochastic inverse dynamics
- generative inverse design
- probabilistic model updating
Signature concepts
- identifiability
- attribution
- posterior geometry
- inverse spectral theory
Open problems
- Given a measured ensemble, can dissipative damping be separated from ensemble decoherence?
- What experiment would distinguish them, and how many nominally identical specimens does it need?
- How should a digital twin report the limits of its own confidence?
Selected papers
- Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems
T. Tripura, A. S. Desai, S. Adhikari, S. Chakraborty · Computers & Structures 281, 107008 · 2023 - A physics-informed neural network enhanced importance sampling for data-free reliability analysis
A. Roy, T. Chatterjee, S. Adhikari · Probabilistic Engineering Mechanics 78, 103701 · 2024 - FRF-based finite element model updating for non-viscous and non-proportionally damped systems
V. Arora, S. Adhikari, K. Vijayan · Journal of Sound and Vibration 552, 117639 · 2023 - Reliability analysis of structures by active learning enhanced sparse Bayesian regression
A. Roy, S. Chakraborty, S. Adhikari · Journal of Engineering Mechanics 149(5) · 2023 - Vibrating carbon nanotube based bio-sensors
S. Adhikari, R. Chowdhury · Physica E · 2009
Foundations
Damping identification, structural model updating, distributed-parameter updating, damage detection, nanomechanical sensing and digital twins. These remain live applications, and the research identity now sits with the inference itself.