Psigda: AI and Quantum Methods for Field Equations
A research programme · 1 October 2026 · Zachariah Roydel Robertson
Psigda is a research programme to find out whether AI or quantum methods can solve the field equations of physics faster than conventional solvers. Its plan is to reproduce a published result, try to improve on it, and publish what it finds.
The first problem: Burgers' equation
Burgers' equation is the classic starter equation for this field. It describes how a wave in a fluid steepens into a shock. It is simple enough to solve on modest cloud hardware, and its exact answer is known, so an AI's answer can be checked against it.
∂u/∂t + u ∂u/∂x = ν ∂²u/∂x²
Here u is the fluid's speed, x is position, t is time and ν is the fluid's viscosity.
The second problem is the Schrödinger equation, the core equation of quantum mechanics. The founding paper that solves Burgers' equation also solves a version of it, which makes it the natural next step toward Psigda's quantum focus.
Four papers, and the order of reproduction
The programme starts with paper 1, using the DeepXDE Burgers demonstration. It is the founding paper of the field, and a ready-made implementation runs in a browser.
| # | Paper | What it shows | Role |
|---|---|---|---|
| 1 | Physics-informed neural networks, Raissi, Perdikaris and Karniadakis, Journal of Computational Physics, 2019 | A neural network can solve an equation by being trained to obey it. Includes Burgers' and Schrödinger examples. | Start here |
| 2 | DeepXDE: a deep learning library for solving differential equations, Lu and colleagues | A free toolkit that implements paper 1, with a Burgers demo checked against a reference answer | The tool |
| 3 | Fourier Neural Operator for Parametric PDEs, Li and colleagues, 2020 | A network that learns a whole family of solutions at once, up to three orders of magnitude faster than traditional solvers on Burgers', Darcy flow and Navier–Stokes | Step two |
| 4 | Variational quantum algorithms for nonlinear problems, Lubasch, Joo, Moinier, Kiffner and Jaksch, Physical Review A, 2020 | Quantum computers solving nonlinear equations, demonstrated on the nonlinear Schrödinger equation with results from an IBM quantum device | The quantum frontier |
The original code for paper 1 is no longer maintained and points users to newer versions, which is why DeepXDE is the better way in.
Method: six weeks
All work runs in browser notebooks (Google Colab, with pip install deepxde), with notebooks and results kept public on GitHub. The quantum stage uses IBM's Qiskit. Every session ends with one line in a log: what changed, and what happened.
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Basics. The one idea behind paper 1: train the network to obey the equation.
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Reproduce. Run the DeepXDE Burgers demo unchanged and record its error against the reference answer. This is the baseline.
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Understand. Change one setting at a time, such as network size or number of training points, and log the effect.
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Improve. Try to beat the baseline: lower error, or the same error with fewer training points or less time.
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Go quantum. Adapt the approach to the Schrödinger example in paper 1.
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Publish. Release the notebook and a write-up: what was tried, what worked, what did not, with the numbers.
From programme to company
Psigda becomes a deep-tech company when it has something no one else has. Three signs mark that point: a result that beats published work on a problem people pay to solve, such as faster fluid or heat simulation; a technical cofounder from physics or machine learning; and a clear customer among engineering, energy or climate modellers who run slow simulations today.