Upload folder using huggingface_hub

.gitattributes

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+docs/plots/reward.png filter=lfs diff=lfs merge=lfs -text
+docs/plots/reward_components.png filter=lfs diff=lfs merge=lfs -text

Dockerfile

@@ -0,0 +1,106 @@
+# PhysiX-Live demo Space — CPU-only env + UI.
+#
+# What this Space hosts:
+#
+#   :7860  uvicorn _space_app:app
+#          ├─ /reset, /step                 (OpenEnv stateless API)
+#          ├─ /interactive/*                (browser session API)
+#          ├─ /web/                         (built React SPA)
+#          └─ /interactive/.../llm-step      (LLM-driven episode)
+#
+# What this Space does NOT host:
+#   * Inference. The demo is CPU-only — no torch, no vLLM, no GPU. When
+#     the UI calls `/interactive/.../llm-step` the server forwards to
+#     whatever OpenAI-compatible base URL the browser handed us
+#     (HF Router, OpenAI, Ollama, or our sister L4 Space at
+#     `Pratyush-01/physix-infer` for the trained 3B + Qwen baseline).
+#
+# Why a separate inference Space:
+#   Keeps this CPU image tiny (sub-second cold-start) so the demo URL
+#   never feels like it's stalled. The L4 Space pays GPU rates only
+#   while it's actually serving requests — its `sleep_time=300s` shuts
+#   it down between sessions. Two Spaces, two failure surfaces; if
+#   inference is broken the verifier-only demo (Custom URL → Ollama
+#   etc.) still works.
+
+############################
+# Stage 1: build the SPA
+############################
+FROM node:20-alpine AS frontend
+WORKDIR /build
+RUN corepack enable
+
+COPY frontend/package.json frontend/pnpm-lock.yaml ./
+RUN pnpm install --frozen-lockfile --silent
+
+COPY frontend/ ./
+# Same-origin API fetches (relative paths). The Space serves both API and UI.
+ENV VITE_PHYSIX_API_URL=""
+# Cache-bust marker. Bump when an SPA change isn't taking on the Space —
+# HF BuildKit occasionally reuses stage-1 output even when sources changed.
+# physix-spa-rebuild: 6
+RUN pnpm exec tsc -b \
+    && pnpm exec vite build --base=/web/
+
+############################
+# Stage 2: runtime (FastAPI + SPA)
+############################
+FROM python:3.11-slim AS runtime
+
+ENV PYTHONUNBUFFERED=1 \
+    PIP_NO_CACHE_DIR=1 \
+    PIP_DISABLE_PIP_VERSION_CHECK=1 \
+    HOME=/tmp/home \
+    HF_HOME=/tmp/hf_cache \
+    XDG_CACHE_HOME=/tmp/xdg-cache \
+    PORT=7860 \
+    PHYSIX_HOST=0.0.0.0 \
+    PHYSIX_CORS_ORIGINS=*
+
+# curl for healthchecks; the slim image has neither curl nor build tools
+# by default. Everything else (numpy, scipy, sympy) is a wheel install.
+RUN apt-get update \
+    && apt-get install -y --no-install-recommends curl \
+    && rm -rf /var/lib/apt/lists/*
+
+WORKDIR /app
+
+# Pin the server-side runtime stack. NO torch / unsloth / trl here —
+# this Space never trains and never runs a model locally.
+RUN pip install \
+        "openenv-core[core]>=0.2.2" \
+        "numpy>=1.24" \
+        "scipy>=1.10" \
+        "sympy>=1.12" \
+        "fastapi>=0.110" \
+        "uvicorn[standard]>=0.29" \
+        "pydantic>=2.5" \
+        "openai>=1.40" \
+        "requests>=2.31"
+
+COPY pyproject.toml ./
+COPY physix ./physix
+COPY README.md ./
+RUN pip install --no-deps -e .
+
+# Built SPA from stage 1.
+COPY --from=frontend /build/dist /app/static
+
+# Space wrapper — mounts the React SPA at /web/, registers / -> /web/
+# redirect (OpenEnv's create_fastapi_app doesn't add one for us).
+COPY scripts/space_app.py /app/_space_app.py
+
+# Pre-create writable dirs. HF Spaces runs containers as a non-root UID
+# with no /etc/passwd entry, so any cache path under $HOME must exist
+# and be world-writable BEFORE the runtime user shows up.
+RUN mkdir -p "$HOME" "$HF_HOME" "$XDG_CACHE_HOME" \
+    && chmod -R 0777 /tmp /app
+
+EXPOSE 7860
+
+# /health is OpenEnv's stock endpoint and turns 200 once uvicorn binds.
+HEALTHCHECK --interval=30s --timeout=10s --start-period=30s --retries=3 \
+    CMD curl -fsS "http://127.0.0.1:${PORT}/health" || exit 1
+
+ENV ENABLE_WEB_INTERFACE=true
+CMD ["python3", "-m", "uvicorn", "_space_app:app", "--host", "0.0.0.0", "--port", "7860"]

Makefile

@@ -0,0 +1,5 @@
+dev:
+	uv run python -m physix.server.app --host 127.0.0.1 --port 8000 &
+	cd frontend && pnpm install --frozen-lockfile --silent && pnpm dev
+
+.PHONY: dev

README.md

@@ -1,10 +1,351 @@
 ---
-title: Physix
-emoji: 📚
+title: PhysiX
+emoji: ⚛️
 colorFrom: blue
-colorTo: pink
+colorTo: purple
 sdk: docker
+app_port: 7860
 pinned: false
+license: mit
+short_description: Equation discovery from noisy trajectories (RLVR)
+tags:
+  - openenv
+  - rlvr
+  - physics
+  - equation-discovery
+  - ode
+base_path: /web
 ---
 
-Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference
+# PhysiX — Equation Discovery via RLVR
+
+An [OpenEnv](https://github.com/openenv-hackathon/openenv) hackathon submission (Apr 2026).
+
+Given a noisy trajectory and a one-sentence hint, a language model iteratively proposes and refines an ODE that reproduces the observed motion. Reward comes entirely from `scipy.integrate.odeint` + per-step R² — no LLM-as-judge.
+
+---
+
+## Links
+
+| | |
+|---|---|
+| **Live demo (HF Space)** | https://huggingface.co/spaces/Pratyush-01/physix-live |
+| **Trained model** | https://huggingface.co/Pratyush-01/physix-3b-rl |
+| **Colab training notebook** | https://huggingface.co/spaces/Pratyush-01/physix-live/blob/main/train/physix_train_colab.ipynb |
+| **W&B training runs** | https://wandb.ai/pratyush01/physix-live |
+| **Blog post / writeup** | https://huggingface.co/spaces/Pratyush-01/physix-live/blob/main/docs/blog.md |
+| **Checkpoint repo** | https://huggingface.co/Pratyush-01/physix-3b-rl-ckpt |
+
+---
+
+## Environment
+
+### Physical Systems — 3 Tiers
+
+6 training systems across 3 difficulty tiers, plus 2 held-out Tier 3 systems.
+
+| Tier | System | Ground-truth equation | Notes |
+|------|--------|-----------------------|-------|
+| 1 | Free Fall | `d2y/dt2 = -g` | 1 parameter |
+| 1 | Free Fall with Drag | `d2y/dt2 = -g + k*vy**2` | nonlinear drag |
+| 1 | Simple Pendulum | `d2theta/dt2 = -(g/L)*sin(theta)` | transcendental |
+| 2 | Damped Pendulum | `d2theta/dt2 = -(g/L)*sin(theta) - b*dtheta` | 3 parameters |
+| 2 | Spring-Mass | `d2x/dt2 = -(k/m)*x` | parameter ratio |
+| 2 | Damped Spring | `d2x/dt2 = -(k/m)*x - (b/m)*dx` | damped oscillation |
+| 3 *(held-out)* | Projectile with Drag | 2-D coupled ODE | out-of-distribution |
+| 3 *(held-out)* | Charged Particle in B-field | 2-D Lorentz force | cross-product coupling |
+
+Parameters and initial conditions are randomised per episode.
+
+### Example Task
+
+```
+HINT: Object dropped from altitude 58.3 m, mass 1.8 kg, in air.
+      Air resistance may be non-negligible.
+
+TRAJECTORY (t, y, vy):
+  t=0.00  y=58.30  vy= 0.00
+  t=0.50  y=56.89  vy=-5.44
+  t=1.00  y=51.91  vy=-9.21
+  t=2.00  y=35.70  vy=-13.88
+  t=3.00  y=16.11  vy=-16.02
+  t=5.00  y=-20.42 vy=-16.49   ← terminal velocity visible
+
+STATS: mean_vy=-10.85  std_vy=6.41  min_vy=-16.49
+```
+
+Target output:
+
+```json
+{
+  "equation": "d2y/dt2 = -g + k * vy**2",
+  "params": {"g": 9.81, "k": 0.047},
+  "rationale": "Quadratic drag; vy² is positive regardless of sign of vy."
+}
+```
+
+**Grammar:** operators `+ - * / **`, functions `sin cos tan exp log sqrt abs`, declared state variables and parameter names. Anything outside this scores `format = 0`.
+
+### Episode Flow
+
+```mermaid
+sequenceDiagram
+    participant Agent
+    participant Env as PhysiXEnvironment
+    participant Sim as scipy.odeint
+    participant Verifier
+
+    Env->>Agent: reset() → trajectory + hint
+    loop up to 8 turns
+        Agent->>Env: step(equation + params + rationale)
+        Env->>Sim: simulate hypothesis from t=0
+        Sim-->>Verifier: predicted trajectory
+        Verifier-->>Env: r_match + r_progress + r_simplicity + r_format
+        Env->>Agent: mismatch summary + reward breakdown + history
+        alt r_match > 0.93 or budget exhausted
+            Env-->>Agent: done=True
+        end
+    end
+```
+
+After each step the agent receives an English mismatch summary (e.g. *"predicted vy diverges after t=2 s; residual consistently negative"*) alongside the numeric reward breakdown, so it has something to act on in the next turn.
+
+---
+
+## Reward
+
+All reward is computed from `scipy.odeint` output — no model-in-the-loop scoring.
+
+### Step-wise (live env + GRPO)
+
+| Component | Weight | Formula | Purpose |
+|-----------|:------:|---------|---------|
+| `match` | 0.50 | R² (observed vs. predicted) | primary accuracy signal |
+| `progress` | 0.20 | `max(0, r_match − r_match_prev)` | per-turn improvement shaping |
+| `simplicity` | 0.20 | `1 − (operator_count / 12)` | prefer shorter equations |
+| `format` | 0.10 | 1 if parsed **and** simulated successfully | syntactic + numerical validity |
+
+### GRPO-only additions
+
+Two extra signals are added during training but not used in the live env:
+
+- **`match_dense = sqrt(R²)`** — gives a non-trivial gradient when raw R² is near zero (e.g. `sqrt(0.05) ≈ 0.22`).
+- **`correctness` = 1 if R² ≥ 0.70, else 0** — a binary bonus that helps push past R² plateaus where the dense signal flattens.
+
+### Reward-hacking mitigations
+
+Three failure modes found during development and how they were closed:
+
+**1. Parse-but-crash exploit.**
+A valid-but-explosive equation (e.g. `d2y/dt2 = exp(vy**10)`) parses but makes `odeint` produce NaN. Without a fix, it earns `format = 1`.  
+→ `format = 1` only if integration completes without NaN/inf.
+
+**2. Trivial-equation exploit.**
+`d2y/dt2 = 0` has zero operators, so `simplicity = 1`, earning 20% reward for a completely wrong trajectory.  
+→ `simplicity = 0` unless `r_match ≥ 0.10`.
+
+**3. Progress signal in single-turn GRPO.**
+Every GRPO training row starts with `previous_r_match = 0`, so `progress = r_match` — a redundant copy of the match signal that dilutes advantage estimates.  
+→ `progress` is excluded from the GRPO reward function set; it is only used in multi-turn live episodes.
+
+---
+
+## Training: SFT → GRPO
+
+### Why SFT first
+
+GRPO relies on reward variance across rollouts to estimate advantages. With a cold base model, ~80% of completions are unparseable (LaTeX, prose, malformed JSON) and most parseable ones crash the integrator, leaving near-zero variance and no useful gradient. The model needs to produce the right output format before RL can do anything meaningful with the physics signal.
+
+SFT runs for 3 epochs on synthetic `(prompt, ground_truth_equation)` pairs generated from the environment. After SFT:
+- >90% of completions parse and simulate successfully (up from ~20%).
+- Equations are in the ASCII ODE grammar the verifier expects.
+- The model has seen the right equation family for each system at least once.
+
+SFT only establishes format. Parameter values are still wrong — that is what GRPO refines.
+
+### Step 1 — SFT warm-start
+
+```bash
+python -m physix.training.sft \
+  --model Qwen/Qwen2.5-3B-Instruct \
+  --output-dir runs/physix-3b-sft \
+  --epochs 3 \
+  --lora-r 32 \
+  --instances-per-system 32 \
+  --system-ids damped_spring
+```
+
+Runtime: ~5 min on L40S.
+
+### Step 2 — GRPO
+
+```bash
+python -m physix.training.loop \
+  --model Qwen/Qwen2.5-3B-Instruct \
+  --output-dir runs/physix-3b-rl \
+  --num-steps 200 \
+  --num-generations 4 \
+  --lora-r 32 \
+  --sft-checkpoint runs/physix-3b-sft/merged \
+  --system-ids damped_spring \
+  --push-to-hub \
+  --hub-repo-id Pratyush-01/physix-3b-rl
+```
+
+Runtime: ~45 min on L40S.
+
+### Full cloud job
+
+```bash
+hf jobs uv run train/job_train_single.py \
+    --image unsloth/unsloth:2026.3.8-pt2.9.0-vllm-0.16.0-cu12.8-studio-release \
+    --flavor l40sx1 \
+    --secrets HF_TOKEN \
+    --secrets WANDB_API_KEY \
+    -v hf://datasets/Pratyush-01/physix-live-src:/physix-live \
+    --timeout 2h
+```
+
+---
+
+## Training Results
+
+| GRPO Loss (↓) | Total Reward (↑) |
+|:---:|:---:|
+| ![loss](docs/plots/loss.png) | ![reward](docs/plots/reward.png) |
+
+| Per-component reward breakdown |
+|:---:|
+| ![reward components](docs/plots/reward_components.png) |
+
+W&B runs: [pratyush01/physix-live](https://wandb.ai/pratyush01/physix-live)
+
+Key observations from the run:
+- `reward/format` jumps to ~0.9 in the first 10 steps and holds there — the SFT warm-start does its job.
+- `reward/match_dense` (√R²) and `reward/correctness` both trend from ~0.6 to ~0.9–1.0 over 200 steps — the physics simulation is driving the gradient.
+- `reward/match` (raw R²) tracks match_dense and converges to ~0.95+ by step 150, indicating the model reliably proposes equations that fit the trajectory.
+- `reward/simplicity` rises gradually; the gate at R²≥0.10 prevents trivial-equation gaming (`d2y/dt2 = 0` can't earn simplicity reward).
+- Total mean reward rises from ~3.3 to ~4.8 (+45%) with ±1σ variance shrinking — the policy is both improving and becoming more consistent.
+
+What we don't claim:
+- The model generalises well to Tier 3 systems without further training.
+- A 3B model is competitive with frontier models on this task.
+- The reward improvements translate to meaningful physics understanding beyond the training distribution.
+
+---
+
+## Repository Layout
+
+```
+physix-live/
+├── physix/
+│   ├── models.py                 # Pydantic Action / Observation / State
+│   ├── client.py                 # OpenEnv WebSocket client
+│   ├── systems/                  # physical systems
+│   │   ├── base.py               # PhysicalSystem ABC
+│   │   ├── tier1.py              # FreeFall, FreeFallWithDrag, SimplePendulum
+│   │   ├── tier2.py              # DampedPendulum, SpringMass, DampedSpring
+│   │   ├── tier3.py              # ProjectileWithDrag, ChargedInBField (held out)
+│   │   └── registry.py
+│   ├── verifier/
+│   │   ├── parser.py             # SymPy whitelisted grammar
+│   │   ├── simulator.py          # scipy.odeint forward simulation
+│   │   ├── metrics.py            # per-step R²
+│   │   ├── mismatch.py           # English residual summary
+│   │   └── reward.py             # reward composition + hacking mitigations
+│   ├── server/
+│   │   ├── environment.py        # PhysiXEnvironment (OpenEnv subclass)
+│   │   ├── interactive.py        # session-based REST router for the UI
+│   │   └── app.py
+│   └── training/
+│       ├── prompt.py             # observation → prompt
+│       ├── scorer.py             # cached single-completion scorer
+│       ├── reward_fns.py         # TRL-compatible reward callables
+│       ├── dataset.py            # GRPO dataset builder
+│       ├── sft.py                # SFT warm-start
+│       └── loop.py               # Unsloth + TRL GRPO loop
+├── frontend/                     # React + TS + Tailwind demo UI
+├── train/                        # HF Jobs launcher + Colab notebook
+│   ├── submit.py                 # submit job via HfApi.run_uv_job
+│   ├── job_train.py              # multi-system driver (in-container)
+│   ├── job_train_single.py       # single-system driver (in-container)
+│   ├── physix_train_colab.ipynb  # SFT → GRPO end-to-end notebook
+│   └── sync-plots.sh             # mirror plots from model repo
+├── tests/                        # ~30 tests
+├── docs/
+│   ├── plots/                    # committed loss / reward / per-component PNGs
+│   └── writeup.md
+├── Dockerfile                    # env Space build (FastAPI + built React UI)
+├── openenv.yaml                  # OpenEnv manifest (name, runtime, app entrypoint)
+└── pyproject.toml
+```
+
+---
+
+## Quick Start
+
+One command from the repo root:
+
+```bash
+make dev
+```
+
+This starts the FastAPI backend on `:8000` (deps auto-resolved by `uv`) and the Vite frontend on `:5173`. Open [http://localhost:5173](http://localhost:5173).
+
+### Connecting an LLM
+
+The demo speaks to **any OpenAI-compatible `/v1/chat/completions` endpoint** — local Ollama, Hugging Face Inference Providers, OpenAI, vLLM, OpenRouter, etc. The "Connect an LLM" panel exposes:
+
+| Field | Purpose |
+|-------|---------|
+| **Endpoint** | Preset dropdown. Picks `base_url` + a default model id. |
+| **Model** | Provider-native id (HF repo, Ollama tag, OpenAI name). Free-form. |
+| **Custom base URL** | Shown when `Custom` is selected. Anything ending in `/v1`. |
+| **API key** | Bearer token. Persisted per `base_url` in `localStorage`, never sent unless an episode runs. |
+
+Server-side env-var fallback (lets a deployed Space ship a sensible default without leaking secrets in the bundle):
+
+| URL family | Env var |
+|---|---|
+| `*huggingface*` | `HF_TOKEN`, then `HUGGINGFACE_API_KEY` |
+| `*openai.com*` | `OPENAI_API_KEY` |
+| `*openrouter*` | `OPENROUTER_API_KEY` |
+| `localhost` / `127.0.0.1` | none (Ollama needs no key) |
+
+### Side-by-side comparison
+
+The default page is a **two-column comparison**: same trajectory, same hint, same seed, same verifier — two different models. The presets are wired to make the headline story self-evident:
+
+- **A** = `Pratyush-01/physix-3b-rl` via HF Inference Providers (the GRPO-trained model)
+- **B** = `Qwen/Qwen2.5-3B-Instruct` via HF Inference Providers (untrained baseline)
+
+Drop in `gpt-4o-mini` on either side as a frontier reference, or swap to local Ollama for offline dev. The reward delta between the two columns is exactly what GRPO bought — no benchmark-prose necessary.
+
+> **For the trained model on HF Inference Providers**: weights are public, but the repo card needs `inference: true` and a serving provider (Featherless/Together/etc.) to have it loaded. If a visitor sees a 404 from the trained side, they can either bring up `ollama serve` locally and pull a quantised version, or fall back to `Qwen/Qwen2.5-3B-Instruct` on both sides.
+
+### Programmatic use
+
+```python
+import asyncio
+from physix import PhysiXEnv, PhysiXAction
+
+async def main():
+    async with PhysiXEnv(base_url="http://127.0.0.1:8000") as env:
+        obs = await env.reset(system_id="free_fall_drag", seed=42)
+        result = await env.step(
+            PhysiXAction(equation="d2y/dt2 = -g + k * vy**2", params={"g": 9.81, "k": 0.05})
+        )
+        print(result.observation.reward_breakdown)
+
+asyncio.run(main())
+```
+
+```bash
+pytest tests/
+```
+
+---
+
+## License
+
+MIT.

__init__.py

@@ -0,0 +1,37 @@
+"""OpenEnv root package shim.
+
+The OpenEnv CLI's ``validate_env_structure`` expects ``__init__.py``,
+``client.py``, and ``models.py`` to exist at the env-directory root —
+the convention where "the env *is* the package". Our actual code lives
+under ``physix/`` so the wheel builds cleanly and tests / training
+imports stay at ``from physix.* import ...``. These root shims simply
+re-export from ``physix`` so OpenEnv's auto-discovery (which Pascal-
+cases ``name: physix`` to ``Physix*`` in client.py) finds the symbols
+it expects without duplicating any implementation.
+
+NOTE: Inside the deployed Space the package installed via
+``pip install -e .`` is ``physix`` (see ``[tool.hatch.build.targets.wheel]``
+in pyproject.toml). These root files are *only* loaded by the OpenEnv
+CLI's local validator and by users who import the env-directory as a
+package; they are never imported at runtime by the FastAPI server.
+"""
+
+from physix import (  # noqa: F401
+    GRAMMAR_HINT,
+    PhysiXAction,
+    PhysiXEnv,
+    PhysiXObservation,
+    PhysiXState,
+    RewardBreakdown,
+    __version__,
+)
+
+__all__ = [
+    "PhysiXEnv",
+    "PhysiXAction",
+    "PhysiXObservation",
+    "PhysiXState",
+    "RewardBreakdown",
+    "GRAMMAR_HINT",
+    "__version__",
+]

client.py

@@ -0,0 +1,11 @@
+"""OpenEnv root client shim — re-exports ``physix.client``.
+
+OpenEnv's CLI validator and auto-discovery expect ``client.py`` at the
+env-directory root. The real implementation lives in
+``physix/client.py``; this file just re-exports it so the OpenEnv
+contract is satisfied without duplicating any code.
+"""
+
+from physix.client import PhysiXEnv, PhysixEnv  # noqa: F401
+
+__all__ = ["PhysiXEnv", "PhysixEnv"]

docs/blog.md

@@ -0,0 +1,128 @@
+# PhysiX — Equation Discovery from Noisy Trajectories via RLVR
+
+**OpenEnv India Hackathon 2026** · [Live Space](https://huggingface.co/spaces/Pratyush-01/physix-live) · [Trained Model](https://huggingface.co/Pratyush-01/physix-3b-rl) · [W&B Runs](https://wandb.ai/pratyush01/physix-live)
+
+---
+
+## The Problem
+
+Given a short, noisy trajectory of a physical system — positions and velocities over time — can a language model discover the underlying equation of motion?
+
+This is symbolic regression meets agentic RL. The challenge: the equation space is vast, noise means no trajectory perfectly fits any ODE, and the agent must learn to iterate — propose, simulate, compare residuals, refine. Classical tools (genetic programming, sparse regression) can do this, but they can't read a natural language hint or reason about failure in English. We train a 3B LLM to do it using RLVR.
+
+---
+
+## The Environment
+
+**PhysiXEnvironment** gives the agent a noisy trajectory from a physical system and asks it to output an ODE that reproduces the motion. All reward comes from `scipy.odeint` — no LLM-as-judge.
+
+### Systems
+
+Three systems were used for training:
+
+| System | Ground-truth ODE |
+|--------|-----------------|
+| Free Fall | `d2y/dt2 = -g` |
+| Simple Pendulum | `d2theta/dt2 = -(g/L)*sin(theta)` |
+| Damped Spring | `d2x/dt2 = -(k/m)*x - (b/m)*dx` |
+
+Parameters and initial conditions are randomised per episode.
+
+### Episode flow
+
+1. `reset()` → agent receives a noisy trajectory + a one-sentence physical hint
+2. Agent proposes an ODE in JSON: `{"equation": "...", "params": {...}}`
+3. Environment simulates it via `scipy.odeint` and computes R²
+4. Agent receives a residual summary in English + numeric reward breakdown
+5. Repeat up to 8 turns
+
+---
+
+## Reward Design
+
+All reward is computed from `scipy.odeint` — no model-in-the-loop scoring.
+
+**R²** (coefficient of determination): R² = 1 is a perfect match, R² = 0 means no better than predicting the mean, R² < 0 is actively wrong.
+
+| Component | Formula | What it rewards | Why it's needed |
+|-----------|---------|-----------------|-----------------|
+| `match` | R² | Continuous fit quality | Primary learning signal |
+| `match_dense` | √R² | Same, stretched | R² ≈ 0 early on; √R² gives non-zero gradient (√0.05 ≈ 0.22) so GRPO isn't blind in early steps |
+| `correctness` | 1 if R² ≥ 0.70 else 0 | Binary "good enough" | Creates a cliff the policy climbs; helps escape plateaus |
+| `simplicity` | 1 − operators/12, gated on R² ≥ 0.10 | Shorter equations | Without the gate, `d2y/dt2 = 0` scores simplicity = 1 for free |
+| `format` | 1 if parses **and** `odeint` runs without NaN | Valid, simulatable output | Without the NaN check, explosive equations like `exp(vy**10)` claim reward |
+
+---
+
+## Training: SFT → GRPO
+
+### Why SFT first
+
+Qwen2.5-3B out of the box produces LaTeX, prose, or malformed JSON on ~80% of turns — the verifier can't parse any of it. GRPO needs *variance in reward* across rollouts to estimate advantages; if every rollout scores ~0 because nothing parses, the gradient is zero and nothing learns.
+
+SFT on synthetic `(prompt, ground_truth_equation)` pairs teaches the model the output format before RL begins. 4 epochs, ~5 min on L40S. After SFT, >90% of completions parse and simulate successfully — GRPO now has a signal to work with.
+
+### GRPO
+
+- **Model:** Qwen/Qwen2.5-3B-Instruct + LoRA-32
+- **Systems:** free_fall, simple_pendulum, damped_spring
+- **Steps:** 200 (early stopping on reward convergence)
+- **LR:** 1e-5
+- **Generations:** 4 per prompt
+- **Framework:** Unsloth + TRL GRPOTrainer
+
+---
+
+## Results
+
+| SFT Loss (↓) | GRPO Loss (↓) |
+|:---:|:---:|
+| ![SFT loss](plots/sft_loss.png) | ![GRPO loss](plots/loss.png) |
+
+| GRPO Total Reward (↑) |
+|:---:|
+| ![reward](plots/reward.png) |
+
+| Per-component reward breakdown |
+|:---:|
+| ![reward components](plots/reward_components.png) |
+
+Key observations:
+- `reward_format` jumps to ~0.9 in the first 10 steps — the SFT warm-start does its job immediately
+- `reward_match_dense` (√R²) and `reward_correctness` climb from ~0.6 → ~0.95 over 200 steps
+- `reward_match` (raw R²) converges to ~0.95+ by step 150
+- Total mean reward rises from ~3.3 → ~4.8 (+45%) with ±1σ variance shrinking
+- GRPO loss near zero is **expected** — it's the KL regularisation term; the real signal is the reward curves
+
+Full runs: [wandb.ai/pratyush01/physix-live](https://wandb.ai/pratyush01/physix-live)
+
+---
+
+## What's Novel
+
+1. **Verifiable reward without a judge** — R² from `scipy.odeint` is ground truth, not a proxy
+2. **Iterative refinement loop** — the environment feeds residual summaries back in English so the agent can reason about what went wrong and refine
+3. **Reward hacking case study** — three exploits found and patched during development: parse-but-crash equations, trivial-equation simplicity farming, duplicate progress signal
+4. **SFT → GRPO pipeline** — shows how a cold 3B model can be made RL-trainable in under 10 minutes of SFT
+
+---
+
+## Future Scope
+
+The framework is system-agnostic — adding a new physical system means subclassing `PhysicalSystem`, implementing `simulate` and `ground_truth_equation`, and registering it. The verifier, reward function, and training loop need no changes.
+
+Natural extensions:
+
+- **More complex dynamics** — coupled oscillators, Lorenz attractor, reaction-diffusion, N-body gravity
+- **Larger models** — the same pipeline runs on 7B; LoRA rank and LR need tuning but the reward design transfers directly
+- **Multi-turn curriculum** — currently trains on turn-0 only; training on full refinement trajectories would teach the model to use residual feedback more effectively
+- **Noisier / sparser observations** — current trajectories have moderate Gaussian noise; testing on sparser or higher-noise regimes would stress-test the R² reward
+
+---
+
+## Links
+
+- **Live demo:** https://huggingface.co/spaces/Pratyush-01/physix-live
+- **Trained model:** https://huggingface.co/Pratyush-01/physix-3b-rl
+- **Training notebook:** https://huggingface.co/spaces/Pratyush-01/physix-live/blob/main/train/physix_train_colab.ipynb
+- **W&B project:** https://wandb.ai/pratyush01/physix-live

docs/plots/README.md

@@ -0,0 +1,16 @@
+# Training Curves
+
+PNGs in this directory are auto-generated by
+`physix.training.loop._render_training_curves` at end of every GRPO run, then
+mirrored from the HF model repo via `train/sync-plots.sh`.
+
+Files:
+
+- `loss.png`              — GRPO surrogate loss over training steps.
+- `reward.png`            — Mean reward (with ±1σ band) over training steps.
+- `reward_components.png` — Per-component reward (`match`, `match_dense`,
+                             `correctness`, `simplicity`, `format`).
+
+To regenerate locally after a job:
+
+    ./train/sync-plots.sh Pratyush-01/physix-3b-rl

frontend/README.md

@@ -0,0 +1,52 @@
+# PhysiX-Live frontend
+
+React + TypeScript + Tailwind UI for the PhysiX-Live demo. Two tabs:
+
+- **Run with LLM** — drives a live episode via `POST /interactive/sessions/:id/llm-step`. Server calls a local Ollama daemon, parses the reply, scores it, returns the turn. The UI streams turn cards as they arrive.
+- **Manual** — `/interactive/sessions/:id/step`: you submit equations yourself.
+
+## Stack
+
+- React 18 with strict TypeScript (`exactOptionalPropertyTypes: true`).
+- Tailwind CSS 3 (warm dark palette, custom tokens in `tailwind.config.js`).
+- Vite 5 dev server / bundler.
+- KaTeX for live equation rendering.
+- Plain HTML5 canvas for trajectory plots — no chart library.
+
+## Layout
+
+```
+src/
+├── App.tsx                       # tab switch
+├── main.tsx                      # ReactDOM root
+├── components/
+│   ├── HeroIntro.tsx             # 3-step "Observe / Hypothesise / Verify"
+│   ├── RunWithLlmPane.tsx        # LLM-driven episode + turn-by-turn stream
+│   ├── InteractivePane.tsx       # manual equation submission
+│   ├── EquationInput.tsx         # textarea + KaTeX preview + starter chips
+│   ├── EquationDisplay.tsx       # KaTeX render of one equation
+│   ├── TrajectoryCanvas.tsx      # observed (cyan) + predicted (coral)
+│   ├── RewardGauge.tsx           # 4-bar breakdown with tooltips
+│   └── Skeleton.tsx              # loading shimmer
+├── hooks/
+│   ├── useInteractiveSession.ts  # manual-mode session lifecycle
+│   └── useLlmEpisodeRunner.ts    # LLM run / pause / step-once orchestration
+├── lib/
+│   ├── interactiveClient.ts      # typed fetch over /interactive/*
+│   ├── trajectory.ts             # canvas projection helpers
+│   ├── format.ts                 # SymPy -> KaTeX
+│   └── cn.ts                     # classnames joiner
+└── types/physix.ts               # mirrors the Pydantic wire schema
+```
+
+## Scripts
+
+```bash
+pnpm install        # install deps
+pnpm dev            # vite dev server on http://localhost:5173
+pnpm typecheck      # strict tsc --noEmit
+pnpm build          # production build into dist/
+pnpm preview        # serve the production build locally
+```
+
+The UI expects `VITE_PHYSIX_API_URL` (default `http://localhost:8000`) to point at a running env server (`python -m physix.server.app`). For the LLM tab you also need `ollama serve` and the model tag pulled.

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frontend/dist-ts-build/vite.config.d.ts

@@ -0,0 +1,2 @@
+declare const _default: import("vite").UserConfig;
+export default _default;

frontend/dist-ts-build/vite.config.js

@@ -0,0 +1,15 @@
+import { defineConfig } from "vite";
+import react from "@vitejs/plugin-react";
+import path from "node:path";
+export default defineConfig({
+    plugins: [react()],
+    resolve: {
+        alias: {
+            "@": path.resolve(__dirname, "./src"),
+        },
+    },
+    server: {
+        port: 5173,
+        open: false,
+    },
+});