What I'm Working On: Neural Surrogates for Physics, Geometry, and Real-Time Simulation

Project set: PINN-Experiments / projects

This section of the site is where I am trying to turn physical processes into learned objects that are small enough to reuse, inspect, benchmark, and present.

The recurring pattern is simple:

1. start with a reference process that is non-neural
2. train a surrogate that learns that process or its geometric or field representation
3. carry the result into a real presentation layer instead of stopping at plots

The presentation layer is usually Taichi GGUI, not because Taichi is the point, but because it forces the result to survive contact with actual geometry, camera, lighting, and motion. If a model is weak, Taichi exposes it immediately. That makes it a useful honesty filter.

This is not one monolithic research program with one architecture repeated seventeen times. It is a set of related experiments around a narrower question:

when does a learned representation stop being "a model that predicts numbers" and become "a usable surrogate for a physical or geometric process"?

Some projects are already published as full posts because they crossed that line. Others are still upstream experiments, recovered prototypes, or technical branches that have not yet earned their own post.

Video Examples

The strongest way to understand the current state of the portfolio is to look at a few representative outputs from the finished branch of the work.

Those four examples cover the strongest current branches:

• cloth as a continuous field
• waves as a continuous field
• PDEs on curved domains
• neural outputs that survive a real geometry-based presentation layer

The Through-Line

There are three recurring interests running through this work.

First, I am interested in representation shifts, not just solver speedups. Several of these projects matter because they change what the object is:

• a wave simulation becomes a continuous field
• a cloth mesh sequence becomes a callable signed-distance function
• a PDE on a curved surface is solved intrinsically rather than on a flattened grid
• a rollout model becomes something that can be treated as geometry instead of only time-series prediction

Second, I care about comparison structure. Most of these projects are intentionally organized as:

• without my model
• with my model
• final Taichi demo

That structure matters because it keeps the learned result tied to a concrete reference instead of letting it float as a pretty animation with no baseline.

Third, I care about visual credibility. I am interested in these projects as research, but I am also interested in them as material for 3D presentation, short-film-adjacent visuals, and more interactive graphics work. That is why the strongest posts lean so hard on fixed-topology geometry, silhouette readability, honest trust windows, and rendering choices that reveal weak structure instead of hiding it.

The Published Projects

Project 01 — GeoPINN on a Sphere

Post · Code

This project is the cleanest statement of the manifold side of the portfolio. The model learns a PDE directly on the unit sphere, with the Laplace-Beltrami operator computed intrinsically on the surface rather than by flattening the problem to a rectangular grid.

What makes it interesting is not just that it looks like a spinning globe. The stronger point is that geometry is part of the solver story from the start. It is the most mathematically explicit project in the set, and it is also the one that most clearly says I care about PDEs on real surfaces, not only on flat toy domains.

Project 05 — ClothGNN

Post · Code

Project 05 is the lightweight end of the cloth-surrogate line: a tiny recurrent GNN that predicts short-horizon cloth dynamics at very high speed. The headline there is not visual richness. It is that a small graph model can compress a cloth process enough to run as something like a real-time inner loop.

In portfolio terms, this is the "speed and compactness" project. It marks one extreme of the design space: very small model, very fast inference, short trustworthy rollout.

Project 08 — HGNN-ClothDyn

Post · Code

Project 08 pushes cloth surrogates in a more hierarchical direction. The idea is that a cloth surface has both local and larger-scale motion, and a hierarchical graph network is a better fit for that than a minimal flat GNN.

This project matters in the portfolio because it sits between the tiny speed-driven graph surrogate of Project 05 and the more ambitious hybrid and implicit-field cloth projects that come later.

Project 09 — HGNN-NIF Cloth

Post · Code

Project 09 is the hybrid attempt: hierarchical graph dynamics plus a neural implicit field decoder. Conceptually, it is one of the most ambitious cloth projects because it tries to combine topology-aware rollout with a continuous representation layer.

It is important to me even though it is not the strongest final visual result, because it exposes a real limit in this line of work: combining good ingredients does not guarantee a good long-horizon surrogate.

Project 12 — NIF-Cloth4D-Temporal

Post · Code

Project 12 stays in the continuous-cloth family, but its real contribution is stricter than "temporal cloth SDF." This is the project where the target, the labels, the extractor, and the final viewer all had to be brought into agreement around the same structural invariant: if the model is going to learn an SDF, then the reference and the evaluation need to behave like one too.

That makes Project 12 important for a different reason than Project 13. It is less about the strongest hero image and more about the discipline of making a continuous-field project honest end to end.

Project 13 — NIF-Cloth4D

Post · Code

Project 13 is the clearest cloth result in the portfolio so far. A cloth sequence becomes a continuous signed-distance function over spacetime, then gets resampled into a stable fixed-topology surface for the final Taichi presentation.

If someone wants the fastest understanding of what I mean by "a neural surrogate that survives both metrics and a real render path," this is one of the first projects I would point to.

Project 17 — WavePINN

Post · Code

Project 17 is the wave-field counterpart to the cloth implicit-field work. Instead of cloth geometry, the learned object is a continuous wave field u(x, z, t), and the final demo treats that field as something that can be resampled and rendered as a surface.

This project matters because it makes the portfolio broader without changing the underlying question. It shows that the representation-shift idea is not cloth-specific.

The Other Projects In The Repo

The published posts are the strongest finished branch of the work. The rest of the repo shows the broader direction of what I am trying to build, even when a project is still exploratory, upstream, or not yet visually mature enough for a full post.

Project 02 — WavePINN-NIF-ComplexMedia

Code

This is the acoustics-side cousin of Project 17: a WavePINN plus neural implicit field stack for acoustic wave propagation in heterogeneous media. The interesting part is not just "another wave project." It is that the repo is set up for spatially varying wave speed fields, different boundary conditions, and more realistic media structure than the cleaner wave demo branch.

If Project 17 is the cleanest finished continuous-wave story, Project 02 is the broader acoustics research branch behind it.

Project 03 — Cell-Path PINNs

Code

Project 03 is the main outlier in the repo. Instead of cloth or fields, it treats trajectories as geodesics on learned potential landscapes. It started from cell-path / chemotaxis framing, but the current implementation is more domain-agnostic: robotics, migration, finance, and game-AI path planning all fit the same formulation.

This project matters because it pushes the portfolio toward learned motion and path geometry rather than only surfaces and scalar fields.

Project 04 — ClothGeom-NIF

Code

Project 04 is archived. It is the static cloth-geometry neural implicit field precursor that fed into later cloth work. The important part now is not the project itself, but what it contributed downstream: mesh extraction utilities, SIREN patterns, and inverse-design pieces that were absorbed into shared modules and the later cloth projects.

It is best read as an ancestor rather than an active branch.

Project 06 — CoastFlow-GNN

Code

Project 06 is the coastal-engineering branch: a multi-scale graph surrogate for coupled wind-wave and coastal flow fields over shoreline and DEM-derived meshes. It sits closer to real-world geospatial simulation than the cleaner cloth and wave demos do.

This branch matters because it tests whether the same surrogate logic can survive much messier geometry, boundary conditions, and forcing structure.

Project 07 — Geom-INR-Motion

Code

Project 07 is the motion-representation branch: continuous-time human motion modeled with SIREN-based implicit neural representations plus curvature and torsion regularization. In other words, instead of asking "can a field represent cloth or waves?" this project asks "can a continuous implicit representation model articulated motion trajectories?"

It is the clearest bridge from the current portfolio into a future character-motion or animation-system direction.

Project 10 — Maxwell-PINN-NIF

Code

Project 10 applies the same general PINN plus implicit-field logic to full-vector Maxwell equations. It is the electromagnetics branch: E and H field prediction with divergence and curl constraints, PML boundaries, and complex media.

Conceptually, this is one of the more serious physics branches in the repo. It has less immediate visual payoff than cloth or water, but it expands the portfolio beyond mechanics into field-based electromagnetics.

Project 11 — NIF-Cloth3D-Interactive

Code

Project 11 is the interactive cloth branch. It is a SIREN-based neural implicit cloth model aimed at real-time inference with Blender integration, artist-facing controls, and arbitrary force conditioning.

Compared with Projects 12 and 13, this branch leans more toward tool use and interactive control than toward the cleanest final geometry-demo result.

Project 14 — PEGNN-Deform

Code

Project 14 is the deformable-body branch: a physics-encoded graph neural network intended to replace finite-element or soft-body simulation loops. Instead of cloth specifically, the target is a broader deformable-body story with energy conservation and structured message passing.

This is one of the branches that could eventually connect more directly to character, body, or soft-tissue deformation pipelines.

Project 15 — PINN-Lite-Foil

Code

Project 15 is the compressed aerodynamics branch: an edge-deployable PINN for 2D airfoil flow prediction with knowledge distillation and ONNX deployment. Its main contribution is not a strong cinematic image. It is the compression and deployment story: how small and fast a physics-informed model can become without losing too much utility.

If Project 05 is the compact cloth surrogate, Project 15 is the compact flow surrogate.

Project 16 — SurfPINN

Code

Project 16 is the free-surface water branch with a dual Eulerian-Lagrangian design. One branch predicts grid-based height fields. The other predicts particle trajectories. The key idea is to keep both views of the surface in play at once rather than committing entirely to one representation.

This makes it one of the more interesting representation experiments in the repo, even though it is still less finished than the strongest published projects.

How The Projects Relate

The easiest way to read the repo is not by date, but by family.

1. Geometry on curved domains

• Project 01

This is the manifold and intrinsic-geometry branch.

2. Cloth as graph rollout

• Projects 05, 08, 09

This is the graph-surrogate branch. These projects are closer to "predict the next cloth state on a fixed mesh." They are valuable because they make rollout stability, trust windows, model size, and topology-aware dynamics very concrete.

3. Cloth as a continuous field

• Projects 11, 12, 13

This is the neural-implicit cloth branch. These are the projects where cloth stops being only a sequence of meshes and becomes something closer to a field that can be queried, re-extracted, or conditioned interactively.

4. Waves and free surfaces as continuous fields

• Projects 02, 16, 17

This is the fluid and wave branch. The main question here is how far a learned field or hybrid surface representation can go before the presentation layer exposes structural weakness.

5. Broader physical deformation and motion

• Projects 07, 14

This is the motion and deformable-body branch.

6. Other physically informed domains

• Projects 03, 06, 10, 15

This is the wider expansion branch: trajectories, coastal flows, electromagnetics, and aerodynamic compression.

What This Portfolio Is Actually About

If I compress the whole section into a few claims, they are these.

1. I am interested in learned surrogates that survive contact with geometry

A model that looks fine in a loss curve but falls apart when mapped to a surface is not enough for what I want. The reason Taichi shows up so often here is that it forces the learned result into a geometry-based presentation.

2. I am interested in continuous representations

Projects 12, 13, and 17 are especially important to me because they move from stored samples to callable fields. That is a real shift in what the learned object is. It changes rendering, sampling, interpolation, and eventually interaction.

3. I am interested in the boundary between research and presentation

These are research projects, but they are also experiments in how research artifacts become things you can actually show, explain, and reuse. I care about the translation layer from:

• notebook or checkpoint

to:

• demo
• post
• visual artifact
• reusable representation

4. I am not only interested in success stories

Some of the graph-rollout projects are here not because they are the strongest visuals, but because they expose real tradeoffs:

• speed vs trust window
• hierarchy vs stability
• hybrid architecture ambition vs long-horizon failure
• representation strength vs extraction honesty

That matters to me. A useful portfolio should show what worked, what almost worked, and what still needs a better representation.

The Current Shape Of The Work

Right now, the strongest through-line in the portfolio is this:

• Project 13 is the clearest cloth hero result
• Project 12 is the clearest example of enforcing a coherent continuous-field contract
• Project 17 is the cleanest continuous-field story outside cloth
• Project 01 is the manifold and intrinsic-geometry branch
• Projects 05, 08, and 09 are the cloth-rollout branch, where the main question is how far graph-based surrogates can go before autoregressive drift becomes the real bottleneck
• Projects 02, 06, 10, 14, 15, and 16 are the broader expansion branches that test how portable these ideas are across other domains
• Projects 03 and 07 point toward motion, trajectory, and animation-adjacent directions beyond the current cloth and field demos

That is the current balance of the work. Some projects are strongest as images. Some are strongest as process. Some are strongest as warnings about what not to trust. Some are strongest as signs of where the portfolio may go next.

Where I Want This To Go

The direction I care about most is not "more demos" in the abstract. It is a tighter convergence between:

• physically meaningful reference processes
• learned surrogates with coherent representations
• geometry or field outputs that can survive strong presentation
• interactive viewing layers that do not break the underlying honesty of the result
• eventually, connections between physical simulation, motion representation, and more film-adjacent graphics work

So if someone reads this section and asks what I am really working on, the answer is:

I am trying to learn when a neural surrogate becomes good enough, coherent enough, and visually stable enough to stand in for a real physical or geometric process rather than only approximate it on paper.

That is the thread connecting all of these projects.