{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulator-in-the-Loop Bayesian Inference with Tesseract\n", "\n", "In this tutorial, you will learn how to use a Tesseract as the forward model inside a [NumPyro](https://num.pyro.ai/) probabilistic programming workflow. We will:\n", "\n", "1. **Wrap a simulator as a Tesseract** — the Lorenz 96 chaotic dynamical system\n", "2. **Embed it in a NumPyro model** — using [tesseract-jax](https://github.com/pasteurlabs/tesseract-jax) to make the Tesseract a native JAX primitive\n", "3. **Run Bayesian inference** — recover posterior distributions over simulator parameters from noisy observations using NUTS (gradient-based MCMC)\n", "4. **Compare gradient strategies** — analytical (JAX autodiff) vs. finite differences vs. gradient-free sampling\n", "\n", "## Why this matters\n", "\n", "Probabilistic programming languages (PPLs) need a forward model they can differentiate through. Connecting a simulator to a PPL usually means writing a custom wrapper that exposes the simulator and its gradients to the sampler by hand. With Tesseract, you wrap the simulator once and it becomes a JAX-differentiable primitive that plugs directly into NumPyro (or any JAX-based PPL). The same Tesseract is also deployable, composable, and reusable in optimization, ML pipelines, and other contexts.\n", "\n", "## The problem\n", "\n", "We have a chaotic dynamical system (Lorenz 96) with an unknown forcing parameter $F$. We observe a noisy, short trajectory and want to recover the posterior distribution $p(F \\mid \\text{observations})$. This is a classic inverse problem that arises in weather forecasting, climate science, and many other fields.\n", "\n", "Because Lorenz 96 is chaotic, the likelihood landscape is rugged for long integration windows. We work with short observation windows where the model response to $F$ is smooth — exactly the regime where gradient-based sampling shines." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:00:26.699352Z", "iopub.status.busy": "2026-07-24T10:00:26.699149Z", "iopub.status.idle": "2026-07-24T10:00:27.645576Z", "shell.execute_reply": "2026-07-24T10:00:27.644496Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Note: you may need to restart the kernel to use updated packages.\n" ] } ], "source": [ "%pip install -r requirements.txt -q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 1: Build and serve the Tesseract\n", "\n", "We use the Lorenz 96 system — a standard benchmark in data assimilation and UQ. This is the *same* JAX-based Tesseract used in the [4D-Var data assimilation demo](data-assimilation.ipynb), living in its `lorenz_tesseract` folder: analytical gradients via `jax.vjp`, with a differentiable forcing parameter $F$. We wrap the simulator once and reuse it here. We also have a `lorenz_tesseract_finitediff` variant that uses pure NumPy and finite-difference gradients, simulating an opaque simulator where source code isn't available." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:00:27.670388Z", "iopub.status.busy": "2026-07-24T10:00:27.670236Z", "iopub.status.idle": "2026-07-24T10:00:30.518354Z", "shell.execute_reply": "2026-07-24T10:00:30.517904Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " [i] Building image ...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ " [i] Built image sha256:863814f6d3d4, ['lorenz:0.1.0', 'lorenz:latest']\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[\"lorenz:0.1.0\", \"lorenz:latest\"]\n" ] } ], "source": [ "%%bash\n", "# Render build status statically instead of an animated spinner,\n", "# which streams as noise in captured notebook output.\n", "export TERM=dumb\n", "tesseract build ../data-assimilation/lorenz_tesseract/" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:00:30.519795Z", "iopub.status.busy": "2026-07-24T10:00:30.519719Z", "iopub.status.idle": "2026-07-24T10:00:32.544309Z", "shell.execute_reply": "2026-07-24T10:00:32.543586Z" } }, "outputs": [], "source": [ "from tesseract_core import Tesseract\n", "\n", "lorenz = Tesseract.from_image(\"lorenz\")\n", "lorenz.serve()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 2: Generate synthetic observations\n", "\n", "We generate ground-truth data by running the Lorenz 96 model with the true forcing $F = 18$, then add Gaussian noise to simulate noisy measurements. We use short observation windows (10 time steps apart) to keep the likelihood landscape well-behaved." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:00:32.547065Z", "iopub.status.busy": "2026-07-24T10:00:32.546815Z", "iopub.status.idle": "2026-07-24T10:00:34.382451Z", "shell.execute_reply": "2026-07-24T10:00:34.382043Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "System dimension: 8\n", "Number of observations: 3\n", "Observations shape: (3, 8)\n" ] } ], "source": [ "import jax\n", "import jax.numpy as jnp\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from tesseract_jax import apply_tesseract\n", "\n", "# Load an initial condition from the two-scale Lorenz 96 system\n", "data = np.load(\"lorenz96_two_scale_F_18_sample_0_small.npz\")\n", "X_states = data[\"X_states\"]\n", "true_trajectory = X_states[500:] # skip transients\n", "X0 = true_trajectory[0]\n", "N_DIM = X0.shape[0] # 8 slow variables\n", "\n", "# Observation setup\n", "OBS_GAP = 10 # time steps between observations\n", "N_OBS = 3 # number of observations\n", "STD_OBS = 0.5 # observation noise standard deviation\n", "TRUE_F = 18.0 # true forcing parameter\n", "N_STEPS = OBS_GAP * N_OBS\n", "\n", "x0_jax = jnp.array(X0, dtype=jnp.float32)\n", "\n", "# Generate ground-truth trajectory with the true F\n", "true_result = apply_tesseract(\n", " lorenz,\n", " {\"state\": x0_jax, \"F\": jnp.float32(TRUE_F), \"dt\": 0.005, \"n_steps\": N_STEPS},\n", ")\n", "true_traj = true_result[\"result\"]\n", "\n", "# Extract states at observation times and add noise\n", "obs_indices = jnp.arange(OBS_GAP - 1, N_STEPS, OBS_GAP)\n", "true_obs = true_traj[obs_indices]\n", "\n", "key = jax.random.PRNGKey(42)\n", "observations = true_obs + STD_OBS * jax.random.normal(key, true_obs.shape)\n", "\n", "print(f\"System dimension: {N_DIM}\")\n", "print(f\"Number of observations: {N_OBS}\")\n", "print(f\"Observations shape: {observations.shape}\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:00:34.383965Z", "iopub.status.busy": "2026-07-24T10:00:34.383841Z", "iopub.status.idle": "2026-07-24T10:00:34.581518Z", "shell.execute_reply": "2026-07-24T10:00:34.581092Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Visualize the ground truth trajectory and observations\n", "fig, axes = plt.subplots(2, 1, figsize=(10, 6), sharex=True)\n", "\n", "for pos, ax in enumerate(axes):\n", " ax.plot(np.array(true_traj[:, pos]), label=f\"True trajectory $X_{pos}$\", color=\"C1\")\n", " ax.plot(\n", " np.array(obs_indices),\n", " np.array(observations[:, pos]),\n", " \"ko\",\n", " ms=6,\n", " label=\"Observations\",\n", " )\n", " ax.set_ylabel(\"Amplitude\")\n", " ax.legend(loc=\"upper right\")\n", "\n", "axes[-1].set_xlabel(\"Time steps\")\n", "axes[0].set_title(f\"Lorenz 96 (F={TRUE_F}) with noisy observations\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 3: Define the NumPyro model\n", "\n", "This is the key integration. We use `apply_tesseract` from [tesseract-jax](https://github.com/pasteurlabs/tesseract-jax) to call the Tesseract as a JAX primitive inside a NumPyro probabilistic model.\n", "\n", "Because `apply_tesseract` registers the Tesseract as a proper JAX operation (with `abstract_eval` and `vector_jacobian_product`), NumPyro's NUTS sampler can differentiate through it automatically. No custom `jax.pure_callback` or `jax.custom_vjp` wiring needed.\n", "\n", "**The model:**\n", "- **Prior:** $F \\sim \\text{Normal}(15, 5)$ — we have a rough idea the forcing is around 10–20\n", "- **Forward model:** Integrate Lorenz 96 from the known initial condition $X_0$ with forcing $F$\n", "- **Likelihood:** $y_i \\sim \\text{Normal}(x_{t_i}, \\sigma_{\\text{obs}})$ — observations are noisy measurements of the state at discrete times" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:00:34.582832Z", "iopub.status.busy": "2026-07-24T10:00:34.582745Z", "iopub.status.idle": "2026-07-24T10:00:35.030078Z", "shell.execute_reply": "2026-07-24T10:00:35.029610Z" } }, "outputs": [], "source": [ "import numpyro\n", "import numpyro.distributions as dist\n", "\n", "\n", "def bayesian_lorenz_model(observations, x0, obs_gap, n_obs, std_obs):\n", " \"\"\"NumPyro model for Bayesian inference over Lorenz 96 forcing parameter.\"\"\"\n", " # Prior on the forcing parameter F\n", " F = numpyro.sample(\"F\", dist.Normal(15.0, 5.0))\n", "\n", " # Forward model: integrate Lorenz 96 using the Tesseract\n", " result = apply_tesseract(\n", " lorenz,\n", " {\n", " \"state\": x0,\n", " \"F\": F,\n", " \"dt\": 0.005,\n", " \"n_steps\": obs_gap * n_obs,\n", " },\n", " )\n", " trajectory = result[\"result\"] # shape: (obs_gap * n_obs, N_DIM)\n", "\n", " # Extract predicted states at observation times\n", " obs_indices = jnp.arange(obs_gap - 1, obs_gap * n_obs, obs_gap)\n", " predicted_obs = trajectory[obs_indices] # shape: (n_obs, N_DIM)\n", "\n", " # Likelihood: observations are noisy measurements of predicted states\n", " numpyro.sample(\n", " \"obs\",\n", " dist.Normal(predicted_obs, std_obs),\n", " obs=observations,\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 4: Run NUTS inference\n", "\n", "NUTS (No-U-Turn Sampler) is a gradient-based MCMC algorithm that uses the gradient of the log-posterior to propose moves. Because `apply_tesseract` is a proper JAX primitive, `jax.grad` flows through the Tesseract automatically — NUTS just works." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:00:35.031496Z", "iopub.status.busy": "2026-07-24T10:00:35.031377Z", "iopub.status.idle": "2026-07-24T10:00:35.035169Z", "shell.execute_reply": "2026-07-24T10:00:35.034752Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Count forward-model evaluations at the Tesseract client boundary.\n", "#\n", "# tesseract-jax calls the served Tesseract's `apply` (forward) and\n", "# `vector_jacobian_product` (gradient) endpoints under the hood. We wrap those\n", "# methods so we can count how often each sampler evaluates the forward model.\n", "#\n", "# For the finite-difference Tesseract, a single VJP call triggers several\n", "# forward evaluations *inside the container* (central differences cost\n", "# 2 evaluations per differentiated input). We account for that separately when\n", "# we report the totals below.\n", "from functools import wraps\n", "\n", "\n", "def instrument(tesseract):\n", " \"\"\"Attach apply/VJP counters to a served Tesseract client (idempotent).\"\"\"\n", " if getattr(tesseract, \"_instrumented\", False):\n", " return tesseract\n", " counts = {\"apply\": 0, \"vjp\": 0}\n", "\n", " def _wrap(name):\n", " orig = getattr(tesseract, name)\n", "\n", " @wraps(orig)\n", " def counted(*args, **kwargs):\n", " counts[\"apply\" if name == \"apply\" else \"vjp\"] += 1\n", " return orig(*args, **kwargs)\n", "\n", " return counted\n", "\n", " tesseract.apply = _wrap(\"apply\")\n", " tesseract.vector_jacobian_product = _wrap(\"vector_jacobian_product\")\n", " tesseract._eval_counts = counts\n", " tesseract._instrumented = True\n", " return tesseract\n", "\n", "\n", "def reset_counts(tesseract):\n", " if getattr(tesseract, \"_instrumented\", False):\n", " tesseract._eval_counts.update(apply=0, vjp=0)\n", "\n", "\n", "instrument(lorenz)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:00:35.036160Z", "iopub.status.busy": "2026-07-24T10:00:35.036101Z", "iopub.status.idle": "2026-07-24T10:01:14.840478Z", "shell.execute_reply": "2026-07-24T10:01:14.839603Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " F 18.00 0.96 18.01 16.57 19.49 220.04 1.00\n", "\n", "Number of divergences: 0\n", "\n", "NUTS wall time: 39.8s\n", "Forward-model calls: 2035 apply + 2034 VJP ≈ 4069 forward evaluations\n", "True F = 18.0\n" ] } ], "source": [ "import time\n", "\n", "from numpyro.infer import MCMC, NUTS\n", "\n", "# Run NUTS\n", "nuts_kernel = NUTS(bayesian_lorenz_model)\n", "mcmc_nuts = MCMC(\n", " nuts_kernel, num_warmup=200, num_samples=500, num_chains=1, progress_bar=False\n", ")\n", "\n", "reset_counts(lorenz)\n", "start = time.time()\n", "mcmc_nuts.run(\n", " jax.random.PRNGKey(0),\n", " observations=observations,\n", " x0=x0_jax,\n", " obs_gap=OBS_GAP,\n", " n_obs=N_OBS,\n", " std_obs=STD_OBS,\n", ")\n", "nuts_time = time.time() - start\n", "\n", "# Each NUTS gradient step evaluates the forward model once (apply) and does one\n", "# reverse-mode VJP; a reverse pass costs roughly one extra forward evaluation.\n", "nuts_counts = dict(lorenz._eval_counts)\n", "nuts_fwd_evals = nuts_counts[\"apply\"] + nuts_counts[\"vjp\"]\n", "\n", "mcmc_nuts.print_summary()\n", "print(f\"\\nNUTS wall time: {nuts_time:.1f}s\")\n", "print(\n", " f\"Forward-model calls: {nuts_counts['apply']} apply + {nuts_counts['vjp']} VJP \"\n", " f\"≈ {nuts_fwd_evals} forward evaluations\"\n", ")\n", "print(f\"True F = {TRUE_F}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 5: Visualize the posterior\n", "\n", "Let's inspect the posterior distribution over $F$. The posterior should be concentrated around the true value $F = 18$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:01:14.845792Z", "iopub.status.busy": "2026-07-24T10:01:14.845695Z", "iopub.status.idle": "2026-07-24T10:01:17.020319Z", "shell.execute_reply": "2026-07-24T10:01:17.019937Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Posterior mean: F = 18.00 ± 0.96\n", "True value: F = 18.0\n" ] } ], "source": [ "import arviz as az\n", "\n", "nuts_samples = mcmc_nuts.get_samples()\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))\n", "\n", "# Trace plot\n", "axes[0].plot(np.array(nuts_samples[\"F\"]), color=\".2\", lw=0.5)\n", "axes[0].axhline(TRUE_F, color=\"C1\", ls=\"--\", label=f\"True F = {TRUE_F}\")\n", "axes[0].set_xlabel(\"Sample\")\n", "axes[0].set_ylabel(\"F\")\n", "axes[0].set_title(\"NUTS trace\")\n", "axes[0].legend()\n", "\n", "# Posterior density\n", "axes[1].hist(np.array(nuts_samples[\"F\"]), bins=30, density=True, color=\".3\", alpha=0.7)\n", "axes[1].axvline(TRUE_F, color=\"C1\", ls=\"--\", lw=2, label=f\"True F = {TRUE_F}\")\n", "axes[1].set_xlabel(\"F\")\n", "axes[1].set_ylabel(\"Density\")\n", "axes[1].set_title(\"Posterior p(F | observations)\")\n", "axes[1].legend()\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "F_mean = float(nuts_samples[\"F\"].mean())\n", "F_std = float(nuts_samples[\"F\"].std())\n", "print(f\"Posterior mean: F = {F_mean:.2f} ± {F_std:.2f}\")\n", "print(f\"True value: F = {TRUE_F}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 6: The opaque simulator scenario\n", "\n", "What if your simulator isn't written in JAX? What if it's a compiled Fortran binary, a commercial solver, or legacy code you can't modify?\n", "\n", "Tesseract handles this too. The `lorenz_tesseract_finitediff` variant implements the same Lorenz 96 physics in **pure NumPy** (no JAX at all) and uses **finite-difference gradients**. From the outside, it exposes the same API — same `apply`, same `vector_jacobian_product` — so the NumPyro model doesn't change at all.\n", "\n", "Let's build and run it." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:01:17.021870Z", "iopub.status.busy": "2026-07-24T10:01:17.021722Z", "iopub.status.idle": "2026-07-24T10:01:19.524143Z", "shell.execute_reply": "2026-07-24T10:01:19.523319Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " [i] Building image ...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ " [i] Built image sha256:9573d754877e, ['lorenz-finitediff:0.1.0', 'lorenz-finitediff:latest']\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[\"lorenz-finitediff:0.1.0\", \"lorenz-finitediff:latest\"]\n" ] } ], "source": [ "%%bash\n", "# Render build status statically instead of an animated spinner,\n", "# which streams as noise in captured notebook output.\n", "export TERM=dumb\n", "tesseract build lorenz_tesseract_finitediff/" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:01:19.526009Z", "iopub.status.busy": "2026-07-24T10:01:19.525907Z", "iopub.status.idle": "2026-07-24T10:01:21.116584Z", "shell.execute_reply": "2026-07-24T10:01:21.115975Z" } }, "outputs": [], "source": [ "lorenz_fd = Tesseract.from_image(\"lorenz-finitediff\")\n", "lorenz_fd.serve()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:01:21.118369Z", "iopub.status.busy": "2026-07-24T10:01:21.118278Z", "iopub.status.idle": "2026-07-24T10:02:25.922128Z", "shell.execute_reply": "2026-07-24T10:02:25.921148Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " F 18.06 1.00 18.02 16.48 19.55 178.70 1.00\n", "\n", "Number of divergences: 0\n", "\n", "NUTS (finite-diff) wall time: 64.8s\n", "Forward-model calls: 2177 apply + 2176 VJP x 2 = 6529 forward evaluations\n", "True F = 18.0\n" ] } ], "source": [ "def bayesian_lorenz_model_fd(observations, x0, obs_gap, n_obs, std_obs):\n", " \"\"\"Same model, but using the finite-difference Tesseract.\"\"\"\n", " F = numpyro.sample(\"F\", dist.Normal(15.0, 5.0))\n", "\n", " result = apply_tesseract(\n", " lorenz_fd,\n", " {\n", " \"state\": x0,\n", " \"F\": F,\n", " \"dt\": 0.005,\n", " \"n_steps\": obs_gap * n_obs,\n", " },\n", " )\n", " trajectory = result[\"result\"]\n", " obs_indices = jnp.arange(obs_gap - 1, obs_gap * n_obs, obs_gap)\n", " predicted_obs = trajectory[obs_indices]\n", "\n", " numpyro.sample(\"obs\", dist.Normal(predicted_obs, std_obs), obs=observations)\n", "\n", "\n", "instrument(lorenz_fd)\n", "\n", "# Run NUTS with finite-diff gradients\n", "nuts_fd_kernel = NUTS(bayesian_lorenz_model_fd)\n", "mcmc_nuts_fd = MCMC(\n", " nuts_fd_kernel,\n", " num_warmup=200,\n", " num_samples=500,\n", " num_chains=1,\n", " progress_bar=False,\n", ")\n", "\n", "reset_counts(lorenz_fd)\n", "start = time.time()\n", "mcmc_nuts_fd.run(\n", " jax.random.PRNGKey(0),\n", " observations=observations,\n", " x0=x0_jax,\n", " obs_gap=OBS_GAP,\n", " n_obs=N_OBS,\n", " std_obs=STD_OBS,\n", ")\n", "nuts_fd_time = time.time() - start\n", "\n", "# The model differentiates only w.r.t. the scalar F, so each finite-difference\n", "# VJP costs 2 forward evaluations inside the container (central differences:\n", "# f(F + eps) and f(F - eps)). Differentiating a higher-dimensional input would\n", "# scale this by 2 * (number of differentiated elements) — which is exactly why\n", "# analytical gradients pull ahead for larger models.\n", "FD_EVALS_PER_VJP = 2 # central differences w.r.t. the single parameter F\n", "nuts_fd_counts = dict(lorenz_fd._eval_counts)\n", "nuts_fd_fwd_evals = nuts_fd_counts[\"apply\"] + FD_EVALS_PER_VJP * nuts_fd_counts[\"vjp\"]\n", "\n", "mcmc_nuts_fd.print_summary()\n", "print(f\"\\nNUTS (finite-diff) wall time: {nuts_fd_time:.1f}s\")\n", "print(\n", " f\"Forward-model calls: {nuts_fd_counts['apply']} apply + \"\n", " f\"{nuts_fd_counts['vjp']} VJP x {FD_EVALS_PER_VJP} \"\n", " f\"= {nuts_fd_fwd_evals} forward evaluations\"\n", ")\n", "print(f\"True F = {TRUE_F}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 7: Gradient-free baseline\n", "\n", "For comparison, let's run a gradient-free sampler. This mirrors the workflow without Tesseract's gradient endpoints — treating the simulator as a black-box function with no derivative information.\n", "\n", "We use NumPyro's Stochastic Approximation (SA) sampler, which doesn't require gradients. To keep the comparison fair on compute, we give SA roughly the same number of forward-model evaluations that NUTS used — each SA iteration is a single forward call. Even with a matched budget, the gradient-free chain struggles to converge." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:02:25.929459Z", "iopub.status.busy": "2026-07-24T10:02:25.929217Z", "iopub.status.idle": "2026-07-24T10:03:02.331496Z", "shell.execute_reply": "2026-07-24T10:03:02.330300Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " F 17.91 1.16 18.22 16.10 19.69 35.09 1.02\n", "\n", "Number of divergences: 0\n", "\n", "SA (gradient-free) wall time: 36.4s\n", "Forward-model calls: 4073 forward evaluations (matched to NUTS budget)\n", "True F = 18.0\n" ] } ], "source": [ "from numpyro.infer import SA\n", "\n", "# SA is gradient-free: it never calls the VJP endpoint, only the forward model.\n", "# To make the comparison fair on compute, we give SA roughly the same number of\n", "# forward evaluations that NUTS used (each SA iteration is one forward call).\n", "sa_total_iters = nuts_fwd_evals\n", "sa_warmup = sa_total_iters // 2\n", "sa_samples_n = sa_total_iters - sa_warmup\n", "\n", "sa_kernel = SA(bayesian_lorenz_model)\n", "mcmc_sa = MCMC(\n", " sa_kernel,\n", " num_warmup=sa_warmup,\n", " num_samples=sa_samples_n,\n", " num_chains=1,\n", " progress_bar=False,\n", ")\n", "\n", "reset_counts(lorenz)\n", "start = time.time()\n", "mcmc_sa.run(\n", " jax.random.PRNGKey(0),\n", " observations=observations,\n", " x0=x0_jax,\n", " obs_gap=OBS_GAP,\n", " n_obs=N_OBS,\n", " std_obs=STD_OBS,\n", ")\n", "sa_time = time.time() - start\n", "\n", "sa_counts = dict(lorenz._eval_counts)\n", "sa_fwd_evals = sa_counts[\"apply\"] + sa_counts[\"vjp\"] # vjp is 0 for SA\n", "\n", "mcmc_sa.print_summary()\n", "print(f\"\\nSA (gradient-free) wall time: {sa_time:.1f}s\")\n", "print(\n", " f\"Forward-model calls: {sa_fwd_evals} forward evaluations (matched to NUTS budget)\"\n", ")\n", "print(f\"True F = {TRUE_F}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 8: Comparison\n", "\n", "Let's compare all three approaches side by side: posterior quality, mixing, and efficiency. Alongside wall time we report the number of forward-model evaluations each method needed. Wall time is machine- and model-dependent, but the forward-evaluation count is the metric that generalizes: it is what grows when the simulator is expensive or the parameter space is high-dimensional." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:03:02.339464Z", "iopub.status.busy": "2026-07-24T10:03:02.339325Z", "iopub.status.idle": "2026-07-24T10:03:02.760143Z", "shell.execute_reply": "2026-07-24T10:03:02.759703Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nuts_fd_samples = mcmc_nuts_fd.get_samples()\n", "sa_samples = mcmc_sa.get_samples()\n", "\n", "fig, axes = plt.subplots(2, 3, figsize=(14, 6))\n", "\n", "configs = [\n", " (\"NUTS (JAX autodiff)\", nuts_samples, nuts_time, nuts_fwd_evals, \"C0\"),\n", " (\"NUTS (finite-diff)\", nuts_fd_samples, nuts_fd_time, nuts_fd_fwd_evals, \"C2\"),\n", " (\"SA (gradient-free)\", sa_samples, sa_time, sa_fwd_evals, \"C3\"),\n", "]\n", "\n", "for i, (label, samples, wall_time, fwd_evals, color) in enumerate(configs):\n", " F_vals = np.array(samples[\"F\"])\n", "\n", " # Trace plot\n", " axes[0, i].plot(F_vals, color=color, lw=0.5, alpha=0.8)\n", " axes[0, i].axhline(TRUE_F, color=\"k\", ls=\"--\", lw=1)\n", " axes[0, i].set_title(f\"{label}\\n({wall_time:.1f}s, {fwd_evals} fwd evals)\")\n", " axes[0, i].set_ylabel(\"F\")\n", " axes[0, i].set_xlabel(\"Sample\")\n", "\n", " # Posterior histogram\n", " axes[1, i].hist(F_vals, bins=30, density=True, color=color, alpha=0.7)\n", " axes[1, i].axvline(TRUE_F, color=\"k\", ls=\"--\", lw=2, label=\"True F\")\n", " axes[1, i].set_xlabel(\"F\")\n", " axes[1, i].set_ylabel(\"Density\")\n", " axes[1, i].legend()\n", "\n", "plt.suptitle(\"Comparison: gradient-based vs gradient-free sampling\", fontsize=13)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:03:02.761742Z", "iopub.status.busy": "2026-07-24T10:03:02.761662Z", "iopub.status.idle": "2026-07-24T10:03:02.769637Z", "shell.execute_reply": "2026-07-24T10:03:02.769152Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Method | Posterior mean | Posterior std | ESS | Wall time (s) | Fwd evals | ESS/sec | ESS/1k evals \n", "---------------------|----------------|---------------|-----|---------------|-----------|---------|--------------\n", " NUTS (JAX autodiff) | 18.00 | 0.96 | 224 | 39.8 | 4069 | 5.6 | 55.1 \n", " NUTS (finite-diff) | 18.06 | 1.00 | 190 | 64.8 | 6529 | 2.9 | 29.1 \n", " SA (gradient-free) | 17.91 | 1.16 | 32 | 36.4 | 4073 | 0.9 | 7.9 \n", "\n", "True F = 18.0\n" ] } ], "source": [ "# Quantitative comparison\n", "def compute_ess(samples):\n", " \"\"\"Compute effective sample size using arviz.\"\"\"\n", " return float(az.ess(samples))\n", "\n", "\n", "results = []\n", "for label, samples, wall_time, fwd_evals, _ in configs:\n", " F_vals = np.array(samples[\"F\"])\n", " ess = compute_ess(F_vals)\n", " results.append(\n", " {\n", " \"Method\": label,\n", " \"Posterior mean\": f\"{F_vals.mean():.2f}\",\n", " \"Posterior std\": f\"{F_vals.std():.2f}\",\n", " \"ESS\": f\"{ess:.0f}\",\n", " \"Wall time (s)\": f\"{wall_time:.1f}\",\n", " \"Fwd evals\": f\"{fwd_evals}\",\n", " \"ESS/sec\": f\"{ess / wall_time:.1f}\",\n", " \"ESS/1k evals\": f\"{1000 * ess / fwd_evals:.1f}\",\n", " }\n", " )\n", "\n", "# Print as a table\n", "header = results[0].keys()\n", "col_widths = {k: max(len(k), max(len(r[k]) for r in results)) + 2 for k in header}\n", "header_str = \"|\".join(k.center(col_widths[k]) for k in header)\n", "sep_str = \"|\".join(\"-\" * col_widths[k] for k in header)\n", "print(header_str)\n", "print(sep_str)\n", "for r in results:\n", " print(\"|\".join(r[k].center(col_widths[k]) for k in header))\n", "\n", "print(f\"\\nTrue F = {TRUE_F}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cleanup" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2026-07-24T10:03:02.770982Z", "iopub.status.busy": "2026-07-24T10:03:02.770879Z", "iopub.status.idle": "2026-07-24T10:03:03.798597Z", "shell.execute_reply": "2026-07-24T10:03:03.797770Z" } }, "outputs": [], "source": [ "lorenz.teardown()\n", "lorenz_fd.teardown()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Takeaways\n", "\n", "1. **Tesseract + tesseract-jax makes simulators first-class citizens in NumPyro.** No custom callbacks, no manual VJP wiring — just `apply_tesseract` inside your model.\n", "\n", "2. **Gradients dramatically improve sampling efficiency.** NUTS with gradients (whether analytical or finite-difference) recovers the true parameter and achieves high ESS, while the gradient-free sampler struggles to converge even when given a matched forward-evaluation budget.\n", "\n", "3. **Count forward evaluations, not just wall time.** Here the model is cheap and we infer a single scalar, so finite-difference NUTS is only modestly more expensive than analytical NUTS — finite differences cost 2 forward evaluations per gradient (central differences w.r.t. one parameter). Differentiating a higher-dimensional input scales that by `2 × (number of parameters)`, while analytical autodiff stays at roughly one forward evaluation per gradient. For costly or high-dimensional models, that gap is what makes analytical gradients decisive.\n", "\n", "4. **Opaque simulators work too.** Even without JAX autodiff, finite-difference gradients via Tesseract's experimental API give NUTS enough information to sample efficiently.\n", "\n", "5. **One Tesseract, many contexts.** The same Lorenz 96 Tesseract we used here is the one from the [4D-Var data assimilation demo](data-assimilation.ipynb) — we only marked its forcing parameter `F` as differentiable. It also works in optimization pipelines and as a deployed service. Wrap once, use everywhere." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What's next\n", "\n", "- **Try a different prior or observation setup.** Adjust `OBS_GAP`, `N_OBS`, or the prior on $F$ to see how data quantity and prior strength shape the posterior.\n", "- **Infer more parameters.** Extend the NumPyro model to recover the initial condition $X_0$ alongside the forcing $F$.\n", "- **Swap the sampler.** Try other gradient-based kernels (e.g. HMC) or run multiple chains to assess convergence.\n", "- **Explore other demos.** The same Lorenz 96 Tesseract also powers the [4D-Var data assimilation demo](data-assimilation.ipynb) — another way to compose Tesseracts with JAX.\n", "\n", "Questions? Feedback? Please reach out through the [Tesseract Community Forum](https://si-tesseract.discourse.group/)." ] } ], "metadata": { "kernelspec": { "display_name": "defaultInterpreterPath: 3.12.7.final.0", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.10" } }, "nbformat": 4, "nbformat_minor": 4 }