inverse design seminar notebooks

Author: yaugenst-flex

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

@@ -0,0 +1,132 @@
+"""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/01_bayes.ipynb

@@ -0,0 +1,73 @@
+{
+  "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
+}

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

@@ -0,0 +1,73 @@
+{
+  "widths_si": [
+    0.4920388608057116,
+    0.5269663382801457,
+    0.47051077631906724,
+    0.45640313960745277,
+    0.4463409120598345,
+    0.479710427467526,
+    0.4926663437517315,
+    0.44457287894940967,
+    0.545014746020923,
+    0.36598776983110565,
+    0.3329813653191155,
+    0.2468853437833761,
+    0.23766189386793363,
+    0.23602095263192163,
+    0.5993116787228173
+  ],
+  "gaps_si": [
+    0.6594384762369605,
+    0.7075580062177993,
+    0.6811015769993951,
+    0.7457468608769762,
+    0.6946555894542846,
+    0.6444157147446795,
+    0.7121732105630795,
+    0.6468550006640721,
+    0.7334476826411184,
+    0.8848483116592654,
+    0.926354310270442,
+    0.9035257883720766,
+    0.8629975364993915,
+    0.8031133570655837,
+    0.7992416233438039
+  ],
+  "widths_sin": [
+    0.8194008890879501,
+    0.654976203326419,
+    0.5154062669153403,
+    0.28937104202011993,
+    0.5797843891332557,
+    0.5547076037062613,
+    0.6077917250899648,
+    0.5628056343171124,
+    0.5933617318869786,
+    0.548751792878745,
+    0.6887370577523546,
+    0.41013832947358364,
+    0.4913432960091517,
+    0.6137520507037625,
+    0.7155681547704924
+  ],
+  "gaps_sin": [
+    0.45753036557675575,
+    0.5098708096717812,
+    0.3,
+    0.49309132198664574,
+    0.5499656317615206,
+    0.6082880193683878,
+    0.6647065648783161,
+    0.6049556315727266,
+    0.48280853554230346,
+    0.45039397074013265,
+    0.7420847046346506,
+    0.6328210425726839,
+    0.5020955912266114,
+    0.3587164271526588,
+    0.5135103145142313
+  ],
+  "first_gap_si": -0.6811767256145679,
+  "first_gap_sin": 0.4802966569812285,
+  "etch_bias_modeled": 0.02
+}