A deep dive into the DeepONets, physics-informed neural networks, and physics-informed DeepONets —

A practice for making reliable model-based predictions — By empowering engineers to reproduce detailed natural processes, computer simulation is transforming the design, analysis, and manufacture of industrial engineering practices. Despite its significant success, one persistent question bothers both analysts and decision-makers: how good are these simulations exactly? Uncertainty quantification, which stands at the confluence of probability, statistics, computational…

A complete LLM project walk-through with code implementation — When I was learning data science and machine learning at university, the curriculum was geared heavily towards algorithms and machine learning techniques. I still remember those days cracking the math, not exactly fun, but nonetheless a rewarding process that had given me a solid foundation. Once I graduated and started…

A project walk-through for the concept, implementation, and demonstration — As a researcher, reading and understanding scientific papers has always been a crucial part of my daily routine. I still remember the tricks I learned in grad school for how to digest a paper efficiently. However, with countless research papers being published every day, I felt overwhelmed to keep up…

A case study with step-by-step code implementation — Differential equations serve as a powerful framework to capture and understand the dynamic behaviors of physical systems. By describing how variables change in relation to each other, they provide insights into system dynamics and allow us to make predictions about the system’s future behavior. However, a common challenge we face…

Active learning for efficiently training parametric PINN — Welcome to the 7th blog post of this series, where we continue our exciting journey of exploring design patterns of physics-informed neural networks (PINN)🙌 In this blog, we will take a closer look at a paper that introduces active learning to PINN. As usual, we will examine the paper through…

Two case studies with parameter estimation and input function calibration — In my previous blog, we delved into the concept of physics-informed DeepONet (PI-DeepONet) and explored why it is particularly suitable for operator learning, i.e., learning mappings from an input function to an output function. …

A step-by-step tutorial on creating a dual-chatbot language learning app with Langchain, OpenAI, gTTS, and Streamlit — When I first began learning a new language, I like to buy those “conversational dialogues” books. I find those books very useful as they help me understand how the language worked — not just the grammar and vocabulary, but also how people really used it in day-to-day life. Now with…

Bring causality to PINN training — Welcome to the 6th blog of this series, where we continue our exciting journey of exploring design patterns of physics-informed neural networks (PINN)🙌 In this episode, we will talk about bringing causality to the training of physics-informed neural nets. As suggested by the paper we will look at today: respecting…