A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problems

Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a neural network to learn a map between infinite dimensional input and output function spaces. These neural operators are trained using a combination of data (observations or simulations) and PDE-residuals (physics-loss). A major drawback of existing neural approaches is the requirement to retrain with new initial/boundary conditions, and the necessity for a large amount of simulation data for training. We develop a physics-informed transformer neural operator (named PINTO) that efficiently generalizes to unseen initial and boundary conditions, trained in a simulation-free setting using only physics loss. The main innovation lies in our new iterative kernel integral operator units, implemented using cross-attention, to transform the PDE solution's domain points into an initial/boundary condition-aware representation vector, enabling efficient learning of the solution function for new scenarios. The PINTO architecture is applied to simulate the solutions of important equations used in engineering applications: advection, Burgers, and steady and unsteady Navier-Stokes equations (three flow scenarios). For these five test cases, we show that the relative errors during testing under challenging conditions of unseen initial/boundary conditions are only one-fifth to one-third of other leading physics informed operator learning methods. Moreover, our PINTO model is able to accurately solve the advection and Burgers equations at time steps that are not included in the training collocation points. The code is available at $\texttt{https://github.com/quest-lab-iisc/PINTO}$

EvalYaks: Instruction Tuning Datasets and LoRA Fine-tuned Models for Automated Scoring of CEFR B2 Speaking Assessment Transcripts

Relying on human experts to evaluate CEFR speaking assessments in an e-learning environment creates scalability challenges, as it limits how quickly and widely assessments can be conducted. We aim to automate the evaluation of CEFR B2 English speaking assessments in e-learning environments from conversation transcripts. First, we evaluate the capability of leading open source and commercial Large Language Models (LLMs) to score a candidate's performance across various criteria in the CEFR B2 speaking exam in both global and India-specific contexts. Next, we create a new expert-validated, CEFR-aligned synthetic conversational dataset with transcripts that are rated at different assessment scores. In addition, new instruction-tuned datasets are developed from the English Vocabulary Profile (up to CEFR B2 level) and the CEFR-SP WikiAuto datasets. Finally, using these new datasets, we perform parameter efficient instruction tuning of Mistral Instruct 7B v0.2 to develop a family of models called EvalYaks. Four models in this family are for assessing the four sections of the CEFR B2 speaking exam, one for identifying the CEFR level of vocabulary and generating level-specific vocabulary, and another for detecting the CEFR level of text and generating level-specific text. EvalYaks achieved an average acceptable accuracy of 96%, a degree of variation of 0.35 levels, and performed 3 times better than the next best model. This demonstrates that a 7B parameter LLM instruction tuned with high-quality CEFR-aligned assessment data can effectively evaluate and score CEFR B2 English speaking assessments, offering a promising solution for scalable, automated language proficiency evaluation.

Automated Educational Question Generation at Different Bloom's Skill Levels using Large Language Models: Strategies and Evaluation

Developing questions that are pedagogically sound, relevant, and promote learning is a challenging and time-consuming task for educators. Modern-day large language models (LLMs) generate high-quality content across multiple domains, potentially helping educators to develop high-quality questions. Automated educational question generation (AEQG) is important in scaling online education catering to a diverse student population. Past attempts at AEQG have shown limited abilities to generate questions at higher cognitive levels. In this study, we examine the ability of five state-of-the-art LLMs of different sizes to generate diverse and high-quality questions of different cognitive levels, as defined by Bloom's taxonomy. We use advanced prompting techniques with varying complexity for AEQG. We conducted expert and LLM-based evaluations to assess the linguistic and pedagogical relevance and quality of the questions. Our findings suggest that LLms can generate relevant and high-quality educational questions of different cognitive levels when prompted with adequate information, although there is a significant variance in the performance of the five LLms considered. We also show that automated evaluation is not on par with human evaluation.

Can Small Language Models Learn, Unlearn, and Retain Noise Patterns?

Small Language Models (SLMs) are generally considered to be more compact versions of large language models (LLMs), typically having fewer than 7 billion parameters. This study investigates the ability of small language models to learn, retain, and subsequently eliminate noise that is typically not found on the internet, where most pretraining datasets are sourced. For this, four pre-trained SLMs were utilized: Olmo 1B, Qwen1.5 1.8B, Gemma 2B, and Phi2 2.7B. The models were instruction-tuned without noise and tested for task execution with in-context learning. Afterward, noise patterns were introduced to evaluate the models' learning and unlearning capabilities. We evaluated the models' performance at various training levels. Phi consistently excelled with word-level noise but performed the worst with character-level noise. Despite being the smallest with approximately 1 billion parameters, Olmo performed consistently well on tasks.

Optimal Path Planning of Autonomous Marine Vehicles in Stochastic Dynamic Ocean Flows using a GPU-Accelerated Algorithm

Autonomous marine vehicles play an essential role in many ocean science and engineering applications. Planning time and energy optimal paths for these vehicles to navigate in stochastic dynamic ocean environments is essential to reduce operational costs. In some missions, they must also harvest solar, wind, or wave energy (modeled as a stochastic scalar field) and move in optimal paths that minimize net energy consumption. Markov Decision Processes (MDPs) provide a natural framework for sequential decision-making for robotic agents in such environments. However, building a realistic model and solving the modeled MDP becomes computationally expensive in large-scale real-time applications, warranting the need for parallel algorithms and efficient implementation. In the present work, we introduce an efficient end-to-end GPU-accelerated algorithm that (i) builds the MDP model (computing transition probabilities and expected one-step rewards); and (ii) solves the MDP to compute an optimal policy. We develop methodical and algorithmic solutions to overcome the limited global memory of GPUs by (i) using a dynamic reduced-order representation of the ocean flows, (ii) leveraging the sparse nature of the state transition probability matrix, (iii) introducing a neighbouring sub-grid concept and (iv) proving that it is sufficient to use only the stochastic scalar field's mean to compute the expected one-step rewards for missions involving energy harvesting from the environment; thereby saving memory and reducing the computational effort. We demonstrate the algorithm on a simulated stochastic dynamic environment and highlight that it builds the MDP model and computes the optimal policy 600-1000x faster than conventional CPU implementations, making it suitable for real-time use.