Aashwin Ananda Mishra

Oliver Hoidn, Aashwin Ananda Mishra, Apurva Mehta

By circumventing the resolution limitations of optics, coherent diffractive imaging (CDI) and ptychography are making their way into scientific fields ranging from X-ray imaging to astronomy. Yet, the need for time consuming iterative phase recovery hampers real-time imaging. While supervised deep learning strategies have increased reconstruction speed, they sacrifice image quality. Furthermore, these methods' demand for extensive labeled training data is experimentally burdensome. Here, we propose an unsupervised physics-informed neural network reconstruction method, PtychoPINN, that retains the factor of 100-to-1000 speedup of deep learning-based reconstruction while improving reconstruction quality by combining the diffraction forward map with real-space constraints from overlapping measurements. In particular, PtychoPINN significantly advances generalizability, accuracy (with a typical 10 dB PSNR increase), and linear resolution (2- to 6-fold gain). This blend of performance and speed offers exciting prospects for high-resolution real-time imaging in high-throughput environments such as X-ray free electron lasers (XFELs) and diffraction-limited light sources.

Roussel Rahman, Aashwin Ananda Mishra

Large Language Models (LLMs) have demonstrated remarkable emergent capabilities, yet the robustness of their numerical reasoning remains an open question. While standard benchmarks evaluate LLM reasoning on complex problem sets using aggregated metrics, they often obscure foundational weaknesses. In this work, we probe LLM mathematical numeracy by evaluating performance on problems of escalating complexity, from constituent operations to combinatorial puzzles. We test several state-of-the-art LLM-based agents on a 100-problem challenge comprising four categories: (1) basic arithmetic, (2) advanced operations, (3) primality checking, and (4) the Game of 24 number puzzle. Our results show that while the agents achieved high accuracy on the first three categories, which require deterministic algorithmic execution, they consistently failed at the number puzzle, underlining its demand for a heuristic search over a large combinatorial space to be a significant bottleneck. These findings reveal that the agents' proficiency is largely confined to recalling and executing known algorithms, rather than performing generative problem-solving. This suggests their apparent numerical reasoning is more akin to sophisticated pattern-matching than flexible, analytical thought, limiting their potential for tasks that require novel or creative numerical insights.

Roussel Rahman, Aashwin Ananda Mishra, Wan-Lin Hu

Both humans and machine learning models learn from experience, particularly in safety- and reliability-critical domains. While psychology seeks to understand human cognition, the field of Explainable AI (XAI) develops methods to interpret machine learning models. This study bridges these domains by applying computational tools from XAI to analyze human learning. We modeled human behavior during a complex real-world task -- tuning a particle accelerator -- by constructing graphs of operator subtasks. Applying techniques such as community detection and hierarchical clustering to archival operator data, we reveal how operators decompose the problem into simpler components and how these problem-solving structures evolve with expertise. Our findings illuminate how humans develop efficient strategies in the absence of globally optimal solutions, and demonstrate the utility of XAI-based methods for quantitatively studying human cognition.

Wai Tong Chung, Aashwin Ananda Mishra, Matthias Ihme

Many practical combustion systems such as those in rockets, gas turbines, and internal combustion engines operate under high pressures that surpass the thermodynamic critical limit of fuel-oxidizer mixtures. These conditions require the consideration of complex fluid behaviors that pose challenges for numerical simulations, casting doubts on the validity of existing subgrid-scale (SGS) models in large-eddy simulations of these systems. While data-driven methods have shown high accuracy as closure models in simulations of turbulent flames, these models are often criticized for lack of physical interpretability, wherein they provide answers but no insight into their underlying rationale. The objective of this study is to assess SGS stress models from conventional physics-driven approaches and an interpretable machine learning algorithm, i.e., the random forest regressor, in a turbulent transcritical non-premixed flame. To this end, direct numerical simulations (DNS) of transcritical liquid-oxygen/gaseous-methane (LOX/GCH4) inert and reacting flows are performed. Using this data, a priori analysis is performed on the Favre-filtered DNS data to examine the accuracy of physics-based and random forest SGS-models under these conditions. SGS stresses calculated with the gradient model show good agreement with the exact terms extracted from filtered DNS. The accuracy of the random-forest regressor decreased when physics-based constraints are applied to the feature set. Results demonstrate that random forests can perform as effectively as algebraic models when modeling subgrid stresses, only when trained on a sufficiently representative database. The employment of random forest feature importance score is shown to provide insight into discovering subgrid-scale stresses through sparse regression.

Wai Tong Chung, Aashwin Ananda Mishra, Nikolaos Perakis et al.

In this investigation, we outline a data-assisted approach that employs random forest classifiers for local and dynamic combustion submodel assignment in turbulent-combustion simulations. This method is applied in simulations of a single-element GOX/GCH4 rocket combustor; a priori as well as a posteriori assessments are conducted to (i) evaluate the accuracy and adjustability of the classifier for targeting different quantities-of-interest (QoIs), and (ii) assess improvements, resulting from the data-assisted combustion model assignment, in predicting target QoIs during simulation runtime. Results from the a priori study show that random forests, trained with local flow properties as input variables and combustion model errors as training labels, assign three different combustion models - finite-rate chemistry (FRC), flamelet progress variable (FPV) model, and inert mixing (IM) - with reasonable classification performance even when targeting multiple QoIs. Applications in a posteriori studies demonstrate improved predictions from data-assisted simulations, in temperature and CO mass fraction, when compared with monolithic FPV calculations. These results demonstrate that this data-driven framework holds promise for the dynamic combustion submodel assignment in reacting flow simulations.