inverse design seminar notebooks

Author: yaugenst-flex

2025-10-09-invdes-seminar/00_setup_guide.ipynb

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+Inverse Design Seminar Demos
+============================
+
+These notebooks track the inverse-designed dual-layer grating coupler workflow presented during the October 9, 2025 seminar. Start with the simulation setup, follow the optimization and robustness studies, and finish with a calibration example that ties measurements back into the digital twin.
+
+Seminar recording: `YouTube link <https://www.youtube.com/watch?v=OpVBJmomzoo>`_
+
+Repository Layout
+-----------------
+- ``00_setup_guide.ipynb`` - builds the baseline Tidy3D simulation for a dual-layer grating coupler and visualizes the initial, uniform geometry.
+- ``01_bayes.ipynb`` - performs a five-parameter Bayesian optimization to locate a high-performing uniform grating without gradient information.
+- ``02_adjoint.ipynb`` - expands to per-tooth parameters and applies adjoint gradients with Adam to apodize the grating and boost peak efficiency.
+- ``03_sensitivity.ipynb`` - quantifies fabrication variability through plus or minus 20 nm bias sweeps, Monte Carlo sampling, and adjoint-based sensitivity analysis.
+- ``04_adjoint_robust.ipynb`` - optimizes the adjoint design against nominal, over, and under etch corners by penalizing performance variance.
+- ``05_robust_comparison.ipynb`` - reruns the Monte Carlo experiment with the robust and nominal designs side by side to measure yield improvements.
+- ``06_measurement_calibration.ipynb`` - demonstrates how adjoint gradients can back-fit SiN widths so simulated spectra line up with measured (synthetic) data.
+
+Supporting assets
+-----------------
+- ``setup.py`` - shared simulation utilities, geometry constraints, and helper routines used across the series.
+- ``optim.py`` - lightweight, autograd-friendly Adam implementation plus parameter clipping helpers.
+- ``results/`` - JSON snapshots of intermediate designs (Bayesian best guess, adjoint refinements, robust solution) consumed by later notebooks.
+
+Getting Started
+---------------
+#. Install dependencies (Python 3.10 or newer recommended):
+
+   .. code-block:: bash
+
+      pip install tidy3d bayes_opt autograd pandas matplotlib scipy
+
+   You also need an active Tidy3D account and API access since every notebook submits jobs with ``tidy3d.web.run``.
+
+#. Launch Jupyter and open the notebooks in numerical order; each one assumes the prior results exist in ``results/``.
+
+Suggested Workflow
+------------------
+- Use ``00_setup_guide.ipynb`` to verify your environment and understand the baseline geometry.
+- Iterate through optimization (``01`` to ``04``) to see how global and local methods complement each other.
+- Leverage the sensitivity and comparison notebooks (``03`` and ``05``) when you need wafer-level statistics.
+- Apply ``06_measurement_calibration.ipynb`` after you gather measured spectra to keep your model synced with hardware.
+
+Enjoy the seminar content, and reach out if you adapt these workflows to your own devices.

2025-10-09-invdes-seminar/01_bayes.ipynb

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+"""Utility routines for functional-style optimization in the tutorial notebooks.
+
+The helpers here avoid mutating inputs so they play nicely with autograd.
+"""
+
+import autograd.numpy as np
+from autograd.misc import flatten
+
+
+def clip_params(params, bounds):
+    """Clip a parameter dictionary according to per-key bounds.
+
+    Parameters
+    ----------
+    params : dict[str, np.ndarray]
+        Dictionary mapping parameter names to array values.
+    bounds : dict[str, tuple[float | None, float | None]]
+        Lower and upper limits for each parameter. Missing keys default to no
+        clipping. ``None`` disables a bound on that side.
+
+    Returns
+    -------
+    dict[str, np.ndarray]
+        New dictionary with values clipped to the requested interval.
+    """
+    clipped = {}
+    for key, value in params.items():
+        lo, hi = bounds.get(key, (None, None))
+        lo_val = -np.inf if lo is None else lo
+        hi_val = np.inf if hi is None else hi
+        clipped[key] = np.clip(value, lo_val, hi_val)
+    return clipped
+
+
+def _flatten(tree):
+    """Return a flat representation of a pytree and its inverse transform."""
+    flat, unflatten = flatten(tree)
+    return np.array(flat, dtype=float), unflatten
+
+
+def init_adam(params, lr=1e-2, beta1=0.9, beta2=0.999, eps=1e-8):
+    """Initialize Adam optimizer state for a parameter pytree.
+
+    Parameters
+    ----------
+    params : dict[str, np.ndarray]
+        Current parameter values used to size the optimizer state.
+    lr : float = 1e-2
+        Learning rate applied to each step.
+    beta1 : float = 0.9
+        Exponential decay applied to the first moment estimate.
+    beta2 : float = 0.999
+        Exponential decay applied to the second moment estimate.
+    eps : float = 1e-8
+        Numerical stabilizer added inside the square-root denominator.
+
+    Returns
+    -------
+    dict[str, object]
+        Dictionary holding the Adam accumulator vectors and hyperparameters.
+    """
+    flat_params, unflatten = _flatten(params)
+    state = {
+        "t": 0,
+        "m": np.zeros_like(flat_params),
+        "v": np.zeros_like(flat_params),
+        "unflatten": unflatten,
+        "lr": lr,
+        "beta1": beta1,
+        "beta2": beta2,
+        "eps": eps,
+    }
+    return state
+
+
+def adam_update(grads, state):
+    """Compute Adam parameter updates from gradients and state.
+
+    Parameters
+    ----------
+    grads : dict[str, np.ndarray]
+        Gradient pytree with the same structure as the parameters.
+    state : dict[str, object]
+        Optimizer state returned by :func:`init_adam`.
+
+    Returns
+    -------
+    updates : dict[str, np.ndarray]
+        Parameter deltas that should be subtracted from the current values.
+    new_state : dict[str, object]
+        Updated optimiser state after incorporating the gradients.
+    """
+    g_flat, _ = _flatten(grads)
+    t = state["t"] + 1
+
+    beta1 = state["beta1"]
+    beta2 = state["beta2"]
+    m = (1 - beta1) * g_flat + beta1 * state["m"]
+    v = (1 - beta2) * (g_flat * g_flat) + beta2 * state["v"]
+
+    m_hat = m / (1 - beta1**t)
+    v_hat = v / (1 - beta2**t)
+    updates_flat = state["lr"] * (m_hat / (np.sqrt(v_hat) + state["eps"]))
+
+    new_state = {
+        **state,
+        "t": t,
+        "m": m,
+        "v": v,
+    }
+    updates = state["unflatten"](updates_flat)
+    return updates, new_state
+
+
+def apply_updates(params, updates):
+    """Apply additive updates to a parameter pytree.
+
+    Parameters
+    ----------
+    params : dict[str, np.ndarray]
+        Original parameter dictionary.
+    updates : dict[str, np.ndarray]
+        Update dictionary produced by :func:`adam_update`.
+
+    Returns
+    -------
+    dict[str, np.ndarray]
+        New dictionary with ``updates`` subtracted element-wise.
+    """
+    p_flat, unflatten = _flatten(params)
+    u_flat, _ = _flatten(updates)
+    return unflatten(p_flat - u_flat)

2025-10-09-invdes-seminar/02_adjoint.ipynb

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+{
+  "widths_si": [
+    0.48262618509355615,
+    0.5207667397076212,
+    0.45559630741287455,
+    0.46361599591364383,
+    0.44415937806339206,
+    0.4725359297284237,
+    0.4897650205171269,
+    0.43401055421044743,
+    0.5470685569556949,
+    0.36090417995022805,
+    0.35112952011499815,
+    0.25182851621035,
+    0.2287991538613288,
+    0.21772272282716135,
+    0.5871457399636976
+  ],
+  "gaps_si": [
+    0.6608377498745214,
+    0.7153002966535659,
+    0.6755416250853287,
+    0.762711911245917,
+    0.6957603543580327,
+    0.6485980725930465,
+    0.7270242877193821,
+    0.6569877864900205,
+    0.7434394276954258,
+    0.8910689853995577,
+    0.92010444487145,
+    0.887662287039533,
+    0.8439724990649012,
+    0.7880932609023489,
+    0.7992416233438039
+  ],
+  "widths_sin": [
+    0.7891411537966333,
+    0.6441362131696193,
+    0.5221408734233975,
+    0.31370712049190075,
+    0.6036396259080945,
+    0.5709134822507435,
+    0.6102929883304251,
+    0.5666814968867978,
+    0.5911545201167835,
+    0.5511240455381605,
+    0.6759490391650566,
+    0.424347404772533,
+    0.4917036091769178,
+    0.5990651442832533,
+    0.7041841301345496
+  ],
+  "gaps_sin": [
+    0.4541255482246594,
+    0.4802605152344745,
+    0.3,
+    0.4914339475589058,
+    0.5480930702315364,
+    0.6026168524939672,
+    0.6561924161853298,
+    0.5934806415337143,
+    0.478494886109227,
+    0.44772190354423175,
+    0.7331937769153588,
+    0.6299485623886972,
+    0.48849470041329063,
+    0.35636407607194925,
+    0.5135103145142313
+  ],
+  "first_gap_si": -0.6720330444742626,
+  "first_gap_sin": 0.5035568088634116,
+  "target_power": 0.5676497430872463
+}