Veera Sundararaghavan

Veera Sundararaghavan, Megna N. Shah, Jeff P. Simmons

The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure. Advanced characterization and physics based simulation techniques have led to generation of extremely large microstructural datasets. There is a need for machine learning techniques that can manage data complexity by capturing the maximal amount of information about the microstructure using the least number of variables. This paper aims to formulate dimensionality and state variable estimation techniques focused on reducing microstructural image data. It is shown that local dimensionality estimation based on nearest neighbors tend to give consistent dimension estimates for natural images for all p-Minkowski distances. However, it is found that dimensionality estimates have a systematic error for low-bit depth microstructural images. The use of Manhattan distance to alleviate this issue is demonstrated. It is also shown that stacked autoencoders can reconstruct the generator space of high dimensional microstructural data and provide a sparse set of state variables to fully describe the variability in material microstructures.

Samuel Onimpa Alfred, Veera Sundararaghavan

We present an autonomous large language model (LLM) agent for end-to-end, data-driven materials theory development. The model can choose an equation form, generate and run its own code, and test how well the theory matches the data without human intervention. The framework combines step-by-step reasoning with expert-supplied tools, allowing the agent to adjust its approach as needed while keeping a clear record of its decisions. For well-established materials relationships such as the Hall-Petch equation and Paris law, the agent correctly identifies the governing equation and makes reliable predictions on new datasets. For more specialized relationships, such as Kuhn's equation for the HOMO-LUMO gap of conjugated molecules as a function of length, performance depends more strongly on the underlying model, with GPT-5 showing better recovery of the correct equation. Beyond known theories, the agent can also suggest new predictive relationships, illustrated here by a strain-dependent law for changes in the HOMO-LUMO gap. At the same time, the results show that careful validation remains essential, because the agent can still return incorrect, incomplete, or inconsistent equations even when the numerical fit appears strong. Overall, these results highlight both the promise and the current limitations of autonomous LLM agents for AI-assisted scientific modeling and discovery.

Veera Sundararaghavan, Megna N. Shah, Jeff P. Simmons

There is a growing attention given to utilizing Lagrangian and Hamiltonian mechanics with network training in order to incorporate physics into the network. Most commonly, conservative systems are modeled, in which there are no frictional losses, so the system may be run forward and backward in time without requiring regularization. This work addresses systems in which the reverse direction is ill-posed because of the dissipation that occurs in forward evolution. The novelty is the use of Morse-Feshbach Lagrangian, which models dissipative dynamics by doubling the number of dimensions of the system in order to create a mirror latent representation that would counterbalance the dissipation of the observable system, making it a conservative system, albeit embedded in a larger space. We start with their formal approach by redefining a new Dissipative Lagrangian, such that the unknown matrices in the Euler-Lagrange's equations arise as partial derivatives of the Lagrangian with respect to only the observables. We then train a network from simulated training data for dissipative systems such as Fickian diffusion that arise in materials sciences. It is shown by experiments that the systems can be evolved in both forward and reverse directions without regularization beyond that provided by the Morse-Feshbach Lagrangian. Experiments of dissipative systems, such as Fickian diffusion, demonstrate the degree to which dynamics can be reversed.

Siddhartha Srivastava, Veera Sundararaghavan

A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. Boltzmann machines are undirected graphs with a network of visible and hidden nodes where the former is used as the reading site while the latter is used to manipulate visible states' probability. In Generative BM, the samples of visible data imitate the probability distribution of a given data set. In contrast, the visible sites of discriminative BM are treated as Input/Output (I/O) reading sites where the conditional probability of output state is optimized for a given set of input states. The cost function for learning BM is defined as a weighted sum of Kullback-Leibler (KL) divergence and Negative conditional Log-Likelihood (NCLL), adjusted using a hyperparamter. Here, the KL Divergence is the cost for generative learning, and NCLL is the cost for discriminative learning. A Stochastic Newton-Raphson optimization scheme is presented. The gradients and the Hessians are approximated using direct samples of BM obtained through Quantum annealing (QA). Quantum annealers are hardware representing the physics of the Ising model that operates on low but finite temperature. This temperature affects the probability distribution of the BM; however, its value is unknown. Previous efforts have focused on estimating this unknown temperature through regression of theoretical Boltzmann energies of sampled states with the probability of states sampled by the actual hardware. This assumes that the control parameter change does not affect the system temperature, however, this is not usually the case. Instead, an approach that works on the probability distribution of samples, instead of the energies, is proposed to estimate the optimal parameter set. This ensures that the optimal set can be obtained from a single run.