PINNs Beyond PDEs: What Changes When the Physics Is Written as an Integral
Most people first encounter PINNs through partial differential equations, and for good reason. PDEs are how physics is usually introduced, analyzed, and benchmarked.
The Boundary Condition Lie: When “Satisfied” Doesn’t Mean “Enforced” in PINNs
Boundary conditions are where physics stops being abstract and becomes accountable. A PDE can be elegant, a loss function can be “decreasing,” a solution can look smooth on a plot — and still be wrong in the one place you actually promised correctness: the boundary.
OpenWebUI Pipelines
Getting Started, Setup, Pitfalls, and First Pipeline
Open WebUI is not just a chat frontend for OpenAI-style APIs—it also supports Pipelines, a plugin framework that lets you add custom logic, RAG workflows, filters, and integrations directly into the system.
Hard vs Soft Boundary Conditions in PINNs: What's the Difference and Why It Matters
In traditional numerical methods, boundary conditions are enforced rigidly — the solution must satisfy them. But in Physics-Informed Neural Networks (PINNs), enforcing boundary conditions is not always straightforward. There are two fundamentally different ways to handle them: hard and soft enforcement.
Why Classic RAG Fails for Scientific Papers — And What To Do Instead
Retrieval-Augmented Generation (RAG) has become the go-to architecture for building intelligent assistants using large language models. It works incredibly well in use cases like customer support