{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "57c34d1a",
   "metadata": {},
   "source": [
    "# nb01 · 선형 연산자로서의 Duhamel / Green 함수\n",
    "\n",
    "**깊게 파기 — Neural Operator · W1**\n",
    "\n",
    "### 이 노트북에서 배우는 것\n",
    "- SDOF 선형 운동방정식의 해 `u(t)`가 지반가속도 `a_g(t)`에 대한 **선형 시불변(LTI) 연산자**의 출력임을 **수치로 증명**한다(선형성 + 시불변성).\n",
    "- 그 연산자를 두 가지로 표현한다: 시간영역 = **Duhamel 적분**(Green 함수 `h`와의 합성곱), 주파수영역 = **전달함수 `H(ω)` 곱셈**. 둘이 수치적으로 일치함을 확인한다.\n",
    "- 이것을 **커널 적분 연산자** `𝒢[p](t)=∫ κ(t,τ) p(τ) dτ` 형태로 쓰고, FNO가 왜 \"주파수영역에서 곱하기\"를 학습하는 구조인지 다리를 놓는다.\n",
    "\n",
    "> 모국어로 말하면: 여기서 \"연산자를 안다\"는 건 구조동역학에서 이미 쓰던 **전달함수 `H(ω)`를 안다**는 말과 같다. FNO는 이 `H(ω)` 자리에 **학습된 복소 가중치**를 넣고 저주파 모드만 남긴, 비선형으로 확장 가능한 버전이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b37c4c80",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-29T09:15:19.050142Z",
     "iopub.status.busy": "2026-10-29T09:15:19.049940Z",
     "iopub.status.idle": "2026-10-29T09:15:19.413173Z",
     "shell.execute_reply": "2026-10-29T09:15:19.412727Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numpy 2.0.2\n"
     ]
    }
   ],
   "source": [
    "# [공통] 라이브러리 로드 + 난수 고정 (재현성)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "rng = np.random.default_rng(0)        # 난수 생성기 고정 → 매번 같은 지진동\n",
    "np.set_printoptions(precision=4, suppress=True)\n",
    "print(\"numpy\", np.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9cc5163",
   "metadata": {},
   "source": [
    "### 1. SDOF 운동방정식과 두 개의 '연산자 표현'\n",
    "\n",
    "지반가진을 받는 단자유도계:\n",
    "$$ m\\,\\ddot u + c\\,\\dot u + k\\,u = -m\\,a_g(t) \\equiv p(t). $$\n",
    "- 고유각진동수 $\\omega_n=\\sqrt{k/m}$, 감쇠비 $\\zeta=c/(2m\\omega_n)$, 감쇠고유각진동수 $\\omega_d=\\omega_n\\sqrt{1-\\zeta^2}$.\n",
    "- **임펄스응답(=Green 함수)**: $h(t)=\\dfrac{1}{m\\,\\omega_d}e^{-\\zeta\\omega_n t}\\sin(\\omega_d t)\\,\\mathbf{1}(t\\ge 0).$\n",
    "- **전달함수**: $H(\\omega)=\\dfrac{1}{k-m\\omega^2+ic\\omega}=\\mathcal{F}\\{h\\}(\\omega).$\n",
    "\n",
    "해는 어느 쪽으로 써도 같다 — 시간영역 합성곱이거나, 주파수영역 곱셈이거나."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0ca2379e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-29T09:15:19.415044Z",
     "iopub.status.busy": "2026-10-29T09:15:19.414842Z",
     "iopub.status.idle": "2026-10-29T09:15:19.418226Z",
     "shell.execute_reply": "2026-10-29T09:15:19.417862Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "wn=12.566 rad/s  k=157.914  c=1.2566  wd=12.551 rad/s\n",
      "dt=0.005s  N=2048  T_total=10.24s\n"
     ]
    }
   ],
   "source": [
    "# [1] 구조 파라미터와 시간축\n",
    "m, zeta = 1.0, 0.05                 # 질량=1 정규화, 감쇠비 5%\n",
    "wn = 2*np.pi*2.0                    # 고유진동수 2 Hz (T=0.5 s)\n",
    "k  = m*wn**2\n",
    "c  = 2*m*zeta*wn\n",
    "wd = wn*np.sqrt(1-zeta**2)\n",
    "\n",
    "dt = 0.005                          # 200 Hz 샘플링\n",
    "N  = 2048                           # 약 10.24 s\n",
    "t  = np.arange(N)*dt\n",
    "print(f\"wn={wn:.3f} rad/s  k={k:.3f}  c={c:.4f}  wd={wd:.3f} rad/s\")\n",
    "print(f\"dt={dt}s  N={N}  T_total={N*dt:.2f}s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e12cb81",
   "metadata": {},
   "source": [
    "### 2. 합성 지진동 — 필터드 화이트노이즈 × Jennings 포락선\n",
    "\n",
    "실제 지진동처럼 보이게: 백색잡음을 밴드패스(대역통과)로 걸러 탁월진동수를 주고, Jennings 형 포락선(상승–정상–지수감쇠)을 곱한다. scipy 없이 numpy FFT만으로 대역통과를 구현한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f084b300",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-29T09:15:19.419723Z",
     "iopub.status.busy": "2026-10-29T09:15:19.419600Z",
     "iopub.status.idle": "2026-10-29T09:15:19.599747Z",
     "shell.execute_reply": "2026-10-29T09:15:19.599365Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a_g shape: (2048,)  peak: 3.0 m/s^2\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x240 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# [2] 합성 지진 지반가속도 a_g(t)\n",
    "def jennings_envelope(t, t_rise=1.5, t_level=4.0, decay=0.25):\n",
    "    e = np.ones_like(t)\n",
    "    e[t < t_rise] = (t[t < t_rise]/t_rise)**2            # 2차 상승\n",
    "    tail = t > (t_rise+t_level)\n",
    "    e[tail] = np.exp(-decay*(t[tail]-(t_rise+t_level)))   # 지수 감쇠\n",
    "    return e\n",
    "\n",
    "def bandpass_fft(x, dt, f_lo=0.5, f_hi=8.0):\n",
    "    # 주파수영역에서 사각 대역만 통과 (교육용 간단 필터)\n",
    "    X = np.fft.rfft(x); f = np.fft.rfftfreq(len(x), dt)\n",
    "    X[(f < f_lo) | (f > f_hi)] = 0.0\n",
    "    return np.fft.irfft(X, n=len(x))\n",
    "\n",
    "def make_ground_motion(rng):\n",
    "    w  = rng.standard_normal(N)\n",
    "    ag = bandpass_fft(w, dt) * jennings_envelope(t)\n",
    "    return ag / np.max(np.abs(ag)) * 3.0                 # 최대 3 m/s^2 로 스케일\n",
    "\n",
    "ag = make_ground_motion(rng)\n",
    "p  = -m*ag                                               # 유효하중 p = -m a_g\n",
    "print(\"a_g shape:\", ag.shape, \" peak:\", np.max(np.abs(ag)).round(3), \"m/s^2\")\n",
    "\n",
    "plt.figure(figsize=(8,2.4)); plt.plot(t, ag, lw=0.8)\n",
    "plt.title(\"synthetic ground acceleration a_g(t)\"); plt.xlabel(\"t [s]\"); plt.ylabel(\"m/s$^2$\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ec51174",
   "metadata": {},
   "source": [
    "### 3. 연산자 표현 A — Duhamel 적분 (커널 적분 = 합성곱)\n",
    "\n",
    "$$ u(t)=\\int_0^t h(t-\\tau)\\,p(\\tau)\\,d\\tau = (h*p)(t). $$\n",
    "시불변이라 커널 $\\kappa(t,\\tau)=h(t-\\tau)$ 는 **차 $t-\\tau$ 에만** 의존한다. 이산화하면 `np.convolve`(이산 합성곱) × `dt`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "39a83be5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-29T09:15:19.654935Z",
     "iopub.status.busy": "2026-10-29T09:15:19.654751Z",
     "iopub.status.idle": "2026-10-29T09:15:19.659633Z",
     "shell.execute_reply": "2026-10-29T09:15:19.659265Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Green h(t) 처음 5개: [0.     0.005  0.0099 0.0148 0.0195]\n",
      "u_duhamel shape: (2048,)  peak disp: 0.02509 m\n"
     ]
    }
   ],
   "source": [
    "# [3] Duhamel = 이산 합성곱\n",
    "def impulse_response(t):\n",
    "    return (1.0/(m*wd))*np.exp(-zeta*wn*t)*np.sin(wd*t)  # Green 함수 h(t), t>=0\n",
    "\n",
    "h = impulse_response(t)\n",
    "def duhamel(p):\n",
    "    # (h * p)[n]*dt, 앞쪽 N개만 취함 → 선형 시불변 연산자 L[p]\n",
    "    return np.convolve(p, h)[:N]*dt\n",
    "\n",
    "u_duh = duhamel(p)\n",
    "print(\"Green h(t) 처음 5개:\", h[:5])\n",
    "print(\"u_duhamel shape:\", u_duh.shape, \" peak disp:\", np.max(np.abs(u_duh)).round(5), \"m\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d914df3",
   "metadata": {},
   "source": [
    "### 4. 연산자 표현 B — 전달함수 곱셈 (주파수영역)\n",
    "\n",
    "합성곱 정리: $U(\\omega)=H(\\omega)\\,P(\\omega)$. 즉 **각 주파수 모드마다 복소수 $H(\\omega)$ 하나를 곱한다.** 이게 FNO Fourier layer의 원형이다 — 다만 FNO는 $H(\\omega)$ 대신 **학습된 복소 가중치**를, 그것도 **저주파 모드에만** 둔다.\n",
    "\n",
    "> ⚠️ **주의(이것도 배울 점):** `rfft`는 신호가 **주기적**이라고 가정한다. 그래서 `irfft(H·rfft(p))`는 Duhamel의 **선형 합성곱**이 아니라 **순환(circular) 합성곱**이다. 우리 계는 감쇠가 5%로 약해 응답이 기록 길이(10 s) 안에 다 사그라들지 않으므로, 순환 합성곱은 꼬리가 앞으로 **감겨 들어와(time aliasing)** 오차가 커진다. 해결: 입력을 **0으로 패딩**해 응답이 다 울려 사라질 공간을 준 뒤 곱한다(그러면 순환=선형이 되어 Duhamel과 일치). 이 '주기성 가정'은 나중에 FNO에서도 그대로 등장한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a9051ae4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-29T09:15:19.661234Z",
     "iopub.status.busy": "2026-10-29T09:15:19.661088Z",
     "iopub.status.idle": "2026-10-29T09:15:19.780354Z",
     "shell.execute_reply": "2026-10-29T09:15:19.779980Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Duhamel vs H(omega) 최대 상대오차: 2.493e-04  (0-패딩 후 수치적으로 동일한 연산자)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# [4] 전달함수 H(omega) 곱셈으로 풀기 (0-패딩으로 순환->선형 합성곱)\n",
    "Npad = 4*N                                    # 응답이 다 울려 사라지도록 충분히 패딩\n",
    "p_pad = np.concatenate([p, np.zeros(Npad-N)])\n",
    "w  = 2*np.pi*np.fft.rfftfreq(Npad, dt)        # 패딩 길이에 맞춘 각진동수 격자\n",
    "H  = 1.0/(k - m*w**2 + 1j*c*w)                # 전달함수 H(omega)\n",
    "U  = H*np.fft.rfft(p_pad)                      # U = H . P  (모드별 복소 곱)\n",
    "u_fft = np.fft.irfft(U, n=Npad)[:N]            # 앞 N개만 = 인과적 응답\n",
    "\n",
    "# 두 연산자 표현의 일치 확인\n",
    "err = np.max(np.abs(u_duh - u_fft))/np.max(np.abs(u_fft))\n",
    "print(\"Duhamel vs H(omega) 최대 상대오차:\", f\"{err:.3e}  (0-패딩 후 수치적으로 동일한 연산자)\")\n",
    "\n",
    "fig, ax = plt.subplots(2,1, figsize=(8,3.6), sharex=True)\n",
    "ax[0].plot(t, u_duh, label=\"Duhamel (h*p)\"); ax[0].plot(t, u_fft, \"--\", label=\"H(w).P (padded)\")\n",
    "ax[0].legend(loc=\"upper right\"); ax[0].set_ylabel(\"u(t) [m]\")\n",
    "ax[1].plot(t, u_duh-u_fft, color=\"crimson\"); ax[1].set_ylabel(\"diff\"); ax[1].set_xlabel(\"t [s]\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "150c12c8",
   "metadata": {},
   "source": [
    "### 5. 이게 '연산자'임을 증명 ① — 선형성\n",
    "\n",
    "연산자 $\\mathcal{L}$ 가 선형이면 임의의 입력 $p_1,p_2$ 와 스칼라 $a,b$ 에 대해\n",
    "$$ \\mathcal{L}[a\\,p_1+b\\,p_2]=a\\,\\mathcal{L}[p_1]+b\\,\\mathcal{L}[p_2]. $$\n",
    "두 지진동을 섞어 넣은 응답과, 각각의 응답을 섞은 것이 같은지 수치로 본다(기계오차 수준이어야 함)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ebe1a797",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-29T09:15:19.781921Z",
     "iopub.status.busy": "2026-10-29T09:15:19.781794Z",
     "iopub.status.idle": "2026-10-29T09:15:19.787228Z",
     "shell.execute_reply": "2026-10-29T09:15:19.786881Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "선형성 상대오차: 3.342e-16 → 0에 가까움 = 선형 연산자 OK\n"
     ]
    }
   ],
   "source": [
    "# [5] 선형성 테스트\n",
    "p1 = -m*make_ground_motion(rng)\n",
    "p2 = -m*make_ground_motion(rng)\n",
    "a_, b_ = 2.3, -1.7\n",
    "\n",
    "lhs = duhamel(a_*p1 + b_*p2)                 # L[a p1 + b p2]\n",
    "rhs = a_*duhamel(p1) + b_*duhamel(p2)        # a L[p1] + b L[p2]\n",
    "lin_err = np.max(np.abs(lhs-rhs))/np.max(np.abs(rhs))\n",
    "print(\"선형성 상대오차:\", f\"{lin_err:.3e}\", \"→ 0에 가까움 = 선형 연산자 OK\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f53b2a98",
   "metadata": {},
   "source": [
    "### 6. 이게 '연산자'임을 증명 ② — 시불변성 (LTI)\n",
    "\n",
    "입력을 시간 $\\Delta$ 만큼 밀면 출력도 똑같이 $\\Delta$ 만큼 밀려야 한다: $\\mathcal{L}[p(t-\\Delta)]=u(t-\\Delta)$. 커널이 차 $t-\\tau$ 에만 의존하는 이유가 바로 이것."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a201adb7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-29T09:15:19.788719Z",
     "iopub.status.busy": "2026-10-29T09:15:19.788606Z",
     "iopub.status.idle": "2026-10-29T09:15:19.792364Z",
     "shell.execute_reply": "2026-10-29T09:15:19.792037Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "시불변성 상대오차: 2.765e-16 → 0에 가까움 = 시불변(LTI) OK\n"
     ]
    }
   ],
   "source": [
    "# [6] 시불변성 테스트 (정수 샘플 shift)\n",
    "shift = 100                                   # 100 샘플 = 0.5 s 지연\n",
    "p_sh  = np.roll(p, shift); p_sh[:shift] = 0.0\n",
    "u_from_shifted = duhamel(p_sh)                # L[p(t-D)]\n",
    "u_shift_then   = np.roll(u_duh, shift); u_shift_then[:shift] = 0.0  # u(t-D)\n",
    "\n",
    "tiv_err = np.max(np.abs(u_from_shifted - u_shift_then))/np.max(np.abs(u_duh))\n",
    "print(\"시불변성 상대오차:\", f\"{tiv_err:.3e}\", \"→ 0에 가까움 = 시불변(LTI) OK\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "013e37c7",
   "metadata": {},
   "source": [
    "### 7. 커널 적분 연산자 형태 → FNO로 가는 다리\n",
    "\n",
    "지금까지를 한 줄로:\n",
    "$$ u=\\mathcal{G}[p],\\qquad \\mathcal{G}[p](t)=\\int \\kappa(t,\\tau)\\,p(\\tau)\\,d\\tau,\\quad \\kappa(t,\\tau)=h(t-\\tau). $$\n",
    "- **선형 + 시불변**이라 커널이 차에만 의존 → 합성곱 → 주파수영역에서 **곱셈** $H(\\omega)$.\n",
    "- **Neural Operator**(Li et al. 2021)는 이 커널 적분을 일반화한다:\n",
    "$$ (\\mathcal{K}v)(x)=\\int \\kappa_\\theta(x,y)\\,v(y)\\,dy. $$\n",
    "  시불변 가정을 쓰면 $\\kappa_\\theta(x,y)=\\kappa_\\theta(x-y)$ 가 되어 합성곱이 되고, 합성곱 정리로 **푸리에영역의 모드별 곱** $R_\\theta(\\omega)\\cdot\\hat v(\\omega)$ 로 바뀐다 — 이게 **Fourier layer**다.\n",
    "- 차이는 둘뿐: (1) $H(\\omega)$ 라는 **고정 물리식** 대신 **학습된 복소 가중치 $R_\\theta$**, (2) 모든 주파수가 아니라 **저주파 모드 몇 개만** 유지(고주파 절단 = 저역통과). 다음 노트북 nb02에서 공식 코드로 바로 확인한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "37b6e60d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-29T09:15:19.793840Z",
     "iopub.status.busy": "2026-10-29T09:15:19.793727Z",
     "iopub.status.idle": "2026-10-29T09:15:19.798876Z",
     "shell.execute_reply": "2026-10-29T09:15:19.798574Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "주파수 분해능 df=0.0977 Hz, 공진 2 Hz 는 약 20번째 모드\n",
      "\n",
      "유지 모드   8개 (~ 0.78 Hz까지) → 기준해 대비 상대오차 9.937e-01\n",
      "유지 모드  16개 (~ 1.56 Hz까지) → 기준해 대비 상대오차 9.707e-01\n",
      "유지 모드  24개 (~ 2.34 Hz까지) → 기준해 대비 상대오차 2.977e-01\n",
      "유지 모드  32개 (~ 3.12 Hz까지) → 기준해 대비 상대오차 8.853e-02\n",
      "유지 모드  64개 (~ 6.25 Hz까지) → 기준해 대비 상대오차 1.957e-02\n",
      "\n",
      "관찰: 공진 모드(~20번)를 포함하는 순간 오차가 급락한다(32모드 이후 수 %).\n",
      "즉 전체 스펙트럼이 아니라 '동역학이 사는 저주파 대역'만 있으면 된다 → FNO가 저모드만 학습/유지하는 근거.\n"
     ]
    }
   ],
   "source": [
    "# [7] '학습된 전달함수'의 직관: 저주파 모드만 남기면? (모드 절단 효과만 분리해서 관찰)\n",
    "# 비교 기준을 '전체 모드 순환해' u_ref로 두면, 패딩 이슈와 무관하게 '모드 절단'만의 영향이 보인다.\n",
    "wN   = 2*np.pi*np.fft.rfftfreq(N, dt)\n",
    "HN   = 1.0/(k - m*wN**2 + 1j*c*wN)\n",
    "P    = np.fft.rfft(p)\n",
    "u_ref = np.fft.irfft(HN*P, n=N)                  # 전체 모드 기준해(순환)\n",
    "df   = 1.0/(N*dt)\n",
    "res_mode = int(round((wn/(2*np.pi))/df))         # 공진(2 Hz)이 놓인 모드 인덱스\n",
    "print(f\"주파수 분해능 df={df:.4f} Hz, 공진 2 Hz 는 약 {res_mode}번째 모드\\n\")\n",
    "for n_modes in [8, 16, 24, 32, 64]:\n",
    "    Hk = HN.copy(); Hk[n_modes:] = 0.0           # 저주파 n_modes개만 유지 (FNO의 모드 절단 흉내)\n",
    "    u_k = np.fft.irfft(Hk*P, n=N)\n",
    "    rel = np.linalg.norm(u_k-u_ref)/np.linalg.norm(u_ref)\n",
    "    print(f\"유지 모드 {n_modes:3d}개 (~{n_modes*df:5.2f} Hz까지) → 기준해 대비 상대오차 {rel:.3e}\")\n",
    "print(\"\\n관찰: 공진 모드(~\"+str(res_mode)+\"번)를 포함하는 순간 오차가 급락한다(32모드 이후 수 %).\")\n",
    "print(\"즉 전체 스펙트럼이 아니라 '동역학이 사는 저주파 대역'만 있으면 된다 → FNO가 저모드만 학습/유지하는 근거.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a9d8c34",
   "metadata": {},
   "source": [
    "### 요약\n",
    "- SDOF 선형 응답은 `a_g → u` 의 **LTI 연산자**이고, 선형성·시불변성을 수치로 확인했다(오차 ~기계정밀도).\n",
    "- 같은 연산자를 **Duhamel 합성곱**(커널 `h`)과 **전달함수 `H(ω)` 곱**으로 쓸 수 있고 둘은 일치한다.\n",
    "- 커널 적분 연산자 $\\mathcal{G}[p]=\\int\\kappa\\,p$ 가 Neural Operator의 출발점이며, 시불변+합성곱정리를 거치면 **푸리에영역 모드별 곱 = Fourier layer**가 된다.\n",
    "- 다음(nb02): 공식 `SpectralConv1d`/`FNO1d`를 그대로 옮겨, `H(ω)` 자리에 **학습 가중치**를 넣고 **Bouc–Wen 비선형** SDOF 지진응답을 예측(smoke run)."
   ]
  }
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