OSCR

Automatic selection of the best neural architecture for time series forecasting.

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6 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 6 matches
  1. [1] § Methods › Composite architectures ↔ Integrated1/NN.py, lines 120–268 · score 0.81 · multi head Attention, hidden state, LSTM block, layer normalization, GRU block, SSM block
  2. [2] § Methods › Composite architectures ↔ Integrated2/NN.py, lines 120–268 · score 0.81 · multi head Attention, hidden state, LSTM block, layer normalization, GRU block, SSM block
  3. [3] § Results › Iterative architecture samplings for glucose prediction task ↔ Process/nsga2_glucose_generations.ipynb, lines 282–399 · score 0.72 · ground truth Pareto, crowding distance, dominated sorting, offspring, canonicalization, seeds
  4. [4] § Results › Iterative architecture samplings for glucose prediction task ↔ Process/nsga2_glucose_generations.ipynb, lines 451–494 · score 0.68 · 5–95 %, ground truth Pareto, band, Discovery, seed, NSGA
  5. [5] § Methods › Multi-objective evolutionary search via NSGA-II › Algorithm 2 ↔ Process/nsga2_glucose_generations.ipynb, lines 102–201 · score 0.61 · binary tournament selection, crowding distance, rank
  6. [6] § Methods › Multi-objective evolutionary search via NSGA-II › Algorithm 2 ↔ Process/nsga2_glucose_generations.ipynb, lines 282–399 · score 0.58 · crowding distance, dominated sorting, rank, fronts, NSGA, Pareto

Paper

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The authors' code

Jupyter notebook · 498 lines · 15 KB · no license · 4 matches

  1. # %% [markdown]
  2. # # NSGA-II (fixed generations) on the glucose architecture dataset (708)
  3. #
  4. # This notebook:
  5. # 1. Loads `data_glucose_2d.pkl` (708 unique architectures).
  6. # 2. Runs **NSGA-II for a fixed number of generations** (e.g., `G=10`) and plots the **Pareto front at generation 10**.
  7. # 3. Repeats NSGA-II for **20 random seeds**, and plots **# of discovered ground-truth Pareto architectures vs. generation** using **mean + 90% band (5–95%)**.
  8. #
  9. # Objectives (to minimize):
  10. # - `rela_error` (relative ℓ2 error)
  11. # - `training_time`
  13. # %%
  14. # Imports
  15. import sys
  16. import pickle
  17. from pathlib import Path
  18. from typing import Dict, List, Tuple, Optional
  20. import numpy as np
  21. import pandas as pd
  22. import matplotlib.pyplot as plt
  24. # %%
  25. # ---------- Robust loading helpers ----------
  26. # Placeholder for the class name used during pickling: "__main__.DataManual"
  27. class DataManual:
  28. def __init__(self, **kwargs):
  29. self.__dict__.update(kwargs)
  31. # Patch NumPy module aliases that can appear in pickles created with other NumPy versions.
  32. import numpy as _np
  33. sys.modules.setdefault("numpy._core", _np.core)
  34. sys.modules.setdefault("numpy._core.multiarray", _np.core.multiarray)
  35. sys.modules.setdefault("numpy._core.numeric", _np.core.numeric)
  36. if hasattr(_np.core, "_multiarray_umath"):
  37. sys.modules.setdefault("numpy._core._multiarray_umath", _np.core._multiarray_umath)
  39. # ---------- Load dataset ----------
  40. pkl_path = "data_glucose_2d.pkl" # if needed, change to the correct path
  42. with open(pkl_path, "rb") as f:
  43. data_loaded = pickle.load(f)
  45. print("Loaded:", type(data_loaded), "len =", len(data_loaded), "example type =", type(data_loaded[0]))
  47. rows = [obj.__dict__.copy() for obj in data_loaded]
  48. df = pd.DataFrame(rows)
  50. # Keep only needed fields (drop param_all)
  51. df = df[[
  52. "n_gru", "n_lstm", "n_attention", "n_ssm",
  53. "dim_hidden", "sequence",
  54. "rela_error", "training_time"
  55. ]].copy()
  57. assert len(df) == 708, "Expected 708 unique architectures."
  58. assert df.isna().sum().sum() == 0, "Found missing values."
  60. obj_cols = ["rela_error", "training_time"]
  61. df.head()
  63. # %% [markdown]
  64. # ## Canonicalization mapping (genotype → unique architecture index)
  65. #
  66. # Even though the dataset already contains 708 unique entries, during NSGA-II we generate children by
  67. # discrete crossover/mutation over the genotype `(counts, sequence, hidden_dim)` and then map back to
  68. # a unique architecture index via a canonical key.
  70. # %%
  71. TEMPLATES = {
  72. 1: ["SSM", "ATT", "GRU", "LSTM"],
  73. 2: ["ATT", "SSM", "GRU", "LSTM"],
  74. 3: ["SSM", "GRU", "ATT", "LSTM"],
  75. 4: ["GRU", "ATT", "SSM", "LSTM"],
  76. 5: ["ATT", "GRU", "SSM", "LSTM"],
  77. 6: ["GRU", "SSM", "ATT", "LSTM"],
  78. }
  79. HIDDEN_SET = [16, 32, 64]
  81. def expand_sequence(n_ssm: int, n_att: int, n_gru: int, n_lstm: int, seq_idx: int) -> Tuple[str, ...]:
  82. order = TEMPLATES[int(seq_idx)]
  83. counts = {"SSM": int(n_ssm), "ATT": int(n_att), "GRU": int(n_gru), "LSTM": int(n_lstm)}
  84. out: List[str] = []
  85. for b in order:
  86. out.extend([b] * counts[b])
  87. return tuple(out)
  89. def canonical_key_from_row(row: pd.Series) -> Tuple[Tuple[str, ...], int]:
  90. seq = expand_sequence(row["n_ssm"], row["n_attention"], row["n_gru"], row["n_lstm"], row["sequence"])
  91. return (seq, int(row["dim_hidden"]))
  93. key_to_idx: Dict[Tuple[Tuple[str, ...], int], int] = {}
  94. for idx, row in df.iterrows():
  95. k = canonical_key_from_row(row)
  96. if k in key_to_idx:
  97. raise ValueError(f"Duplicate canonical key found at idx={idx} and idx={key_to_idx[k]}: {k}")
  98. key_to_idx[k] = int(idx)
  100. print("Unique canonical keys:", len(key_to_idx))
  102. # %% [markdown]
  103. # ## NSGA-II components
  104. # - dominance / Pareto mask
  105. # - fast non-dominated sorting
  106. # - crowding distance
  107. # - binary tournament selection
  109. # %%
  110. def dominates(a: np.ndarray, b: np.ndarray) -> bool:
  111. return np.all(a <= b) and np.any(a < b)
  113. def pareto_mask(objs: np.ndarray) -> np.ndarray:
  114. n = objs.shape[0]
  115. is_eff = np.ones(n, dtype=bool)
  116. for i in range(n):
  117. if not is_eff[i]:
  118. continue
  119. for j in range(n):
  120. if i == j or not is_eff[j]:
  121. continue
  122. if dominates(objs[j], objs[i]):
  123. is_eff[i] = False
  124. break
  125. return is_eff
  127. def fast_non_dominated_sort(pop: List[int], obj: np.ndarray) -> List[List[int]]:
  128. n = len(pop)
  129. S = [[] for _ in range(n)]
  130. n_dom = np.zeros(n, dtype=int)
  131. fronts: List[List[int]] = [[]]
  133. for p in range(n):
  134. for q in range(n):
  135. if p == q:
  136. continue
  137. if dominates(obj[p], obj[q]):
  138. S[p].append(q)
  139. elif dominates(obj[q], obj[p]):
  140. n_dom[p] += 1
  141. if n_dom[p] == 0:
  142. fronts[0].append(p)
  144. i = 0
  145. while fronts[i]:
  146. next_front = []
  147. for p in fronts[i]:
  148. for q in S[p]:
  149. n_dom[q] -= 1
  150. if n_dom[q] == 0:
  151. next_front.append(q)
  152. i += 1
  153. fronts.append(next_front)
  155. if not fronts[-1]:
  156. fronts.pop()
  157. return fronts
  159. def crowding_distance(front: List[int], obj: np.ndarray) -> Dict[int, float]:
  160. if len(front) == 0:
  161. return {}
  162. M = obj.shape[1]
  163. dist = {p: 0.0 for p in front}
  165. for m in range(M):
  166. sorted_front = sorted(front, key=lambda p: obj[p, m])
  167. fmin = obj[sorted_front[0], m]
  168. fmax = obj[sorted_front[-1], m]
  170. dist[sorted_front[0]] = float("inf")
  171. dist[sorted_front[-1]] = float("inf")
  173. if fmax == fmin:
  174. continue
  176. for i in range(1, len(sorted_front) - 1):
  177. prev_p = sorted_front[i - 1]
  178. next_p = sorted_front[i + 1]
  179. dist[sorted_front[i]] += (obj[next_p, m] - obj[prev_p, m]) / (fmax - fmin)
  181. return dist
  183. def tournament_select(pop: List[int], ranks: Dict[int, int], crowds: Dict[int, float], rng: np.random.Generator) -> int:
  184. a = int(rng.integers(0, len(pop)))
  185. b = int(rng.integers(0, len(pop)))
  186. while b == a:
  187. b = int(rng.integers(0, len(pop)))
  189. ia = pop[a]
  190. ib = pop[b]
  191. ra = ranks[ia]
  192. rb = ranks[ib]
  194. if ra < rb:
  195. return ia
  196. if rb < ra:
  197. return ib
  199. ca = crowds.get(ia, 0.0)
  200. cb = crowds.get(ib, 0.0)
  201. return ia if ca >= cb else ib
  203. # %% [markdown]
  204. # ## Variation operators (discrete genotype)
  205. #
  206. # Genotype:
  207. # \[
  208. # (n_{\text{ssm}}, n_{\text{att}}, n_{\text{gru}}, n_{\text{lstm}}, \text{sequence}, \text{dim\_hidden})
  209. # \]
  211. # %%
  212. Genotype = Tuple[int, int, int, int, int, int]
  214. def row_to_genotype(row: pd.Series) -> Genotype:
  215. return (
  216. int(row["n_ssm"]),
  217. int(row["n_attention"]),
  218. int(row["n_gru"]),
  219. int(row["n_lstm"]),
  220. int(row["sequence"]),
  221. int(row["dim_hidden"]),
  222. )
  224. def repair_genotype(g: Genotype, rng: np.random.Generator) -> Genotype:
  225. n_ssm, n_att, n_gru, n_lstm, seq, h = g
  226. n_ssm = int(np.clip(n_ssm, 0, 2))
  227. n_att = int(np.clip(n_att, 0, 2))
  228. n_gru = int(np.clip(n_gru, 0, 2))
  229. n_lstm = int(np.clip(n_lstm, 0, 2))
  230. seq = int(np.clip(seq, 1, 6))
  231. if h not in HIDDEN_SET:
  232. h = int(rng.choice(HIDDEN_SET))
  233. if (n_ssm + n_att + n_gru + n_lstm) == 0:
  234. j = int(rng.integers(0, 4))
  235. if j == 0: n_ssm = 1
  236. if j == 1: n_att = 1
  237. if j == 2: n_gru = 1
  238. if j == 3: n_lstm = 1
  239. return (n_ssm, n_att, n_gru, n_lstm, seq, h)
  241. def canonicalize_to_index(g: Genotype) -> Optional[int]:
  242. n_ssm, n_att, n_gru, n_lstm, seq, h = g
  243. key = (expand_sequence(n_ssm, n_att, n_gru, n_lstm, seq), int(h))
  244. return key_to_idx.get(key, None)
  246. def uniform_crossover(g1: Genotype, g2: Genotype, rng: np.random.Generator) -> Genotype:
  247. child = []
  248. for a, b in zip(g1, g2):
  249. child.append(int(a) if rng.random() < 0.5 else int(b))
  250. return tuple(child) # type: ignore
  252. def mutate_genotype(g: Genotype, rng: np.random.Generator) -> Genotype:
  253. n_ssm, n_att, n_gru, n_lstm, seq, h = g
  254. choice = int(rng.integers(0, 6))
  255. if choice in [0, 1, 2, 3]:
  256. delta = int(rng.choice([-1, 1]))
  257. if choice == 0: n_ssm += delta
  258. if choice == 1: n_att += delta
  259. if choice == 2: n_gru += delta
  260. if choice == 3: n_lstm += delta
  261. elif choice == 4:
  262. seq = int(rng.integers(1, 7))
  263. else:
  264. h = int(rng.choice(HIDDEN_SET))
  265. return (n_ssm, n_att, n_gru, n_lstm, seq, h)
  267. def make_child(parent1_idx: int, parent2_idx: int, rng: np.random.Generator,
  268. p_c: float, p_m: float) -> Genotype:
  269. g1 = row_to_genotype(df.loc[parent1_idx])
  270. g2 = row_to_genotype(df.loc[parent2_idx])
  272. if rng.random() < p_c:
  273. child = uniform_crossover(g1, g2, rng)
  274. else:
  275. child = g1 if rng.random() < 0.5 else g2
  277. if rng.random() < p_m:
  278. child = mutate_genotype(child, rng)
  280. return repair_genotype(child, rng)
  282. # %% [markdown]
  283. # ## NSGA-II run for a fixed number of generations
  284. #
  285. # - Generation 0: after initialization (evaluate `P` architectures)
  286. # - Generation `g>=1`: after producing and evaluating up to `P` new offspring
  288. # %%
  289. def nsga2_run_generations(
  290. G: int = 10,
  291. P: int = 24,
  292. p_c: float = 0.9,
  293. p_m: float = 0.2,
  294. seed: int = 0,
  295. ) -> Dict:
  296. rng = np.random.default_rng(seed)
  297. all_indices = df.index.to_numpy()
  299. # Ground-truth Pareto set from all 708
  300. all_objs = df[obj_cols].to_numpy(dtype=float)
  301. true_pareto_idx = df.index[pareto_mask(all_objs)].to_numpy()
  302. true_pareto_set = set(map(int, true_pareto_idx))
  304. def current_pareto_in_evaluated(evaluated_set: set) -> List[int]:
  305. E_list = sorted(evaluated_set)
  306. E_objs = df.loc[E_list, obj_cols].to_numpy(dtype=float)
  307. mask = pareto_mask(E_objs)
  308. return [E_list[i] for i, ok in enumerate(mask) if ok]
  310. def true_pareto_found_in_evaluated(evaluated_set: set) -> int:
  311. return len(set(evaluated_set) & true_pareto_set)
  313. # initialization
  314. pop = rng.choice(all_indices, size=P, replace=False).tolist()
  315. evaluated = set(int(i) for i in pop)
  317. history = []
  318. history.append({
  319. "gen": 0,
  320. "evaluated_idx": sorted(evaluated),
  321. "pareto_idx": current_pareto_in_evaluated(evaluated),
  322. "true_pareto_found": true_pareto_found_in_evaluated(evaluated),
  323. })
  325. for gen in range(1, G + 1):
  326. pop_objs = df.loc[pop, obj_cols].to_numpy(dtype=float)
  327. fronts = fast_non_dominated_sort(pop, pop_objs)
  329. ranks: Dict[int, int] = {}
  330. crowds: Dict[int, float] = {}
  331. for k, front_pos in enumerate(fronts, start=1):
  332. for ppos in front_pos:
  333. ranks[int(pop[ppos])] = k
  334. cd = crowding_distance(front_pos, pop_objs)
  335. for ppos, dist in cd.items():
  336. crowds[int(pop[ppos])] = float(dist)
  338. # offspring generation
  339. offspring: List[int] = []
  340. attempts = 0
  341. max_attempts = 3000
  343. while len(offspring) < P:
  344. attempts += 1
  345. if attempts > max_attempts:
  346. remaining = list(set(map(int, all_indices)) - evaluated - set(offspring))
  347. if not remaining:
  348. break
  349. offspring.append(int(rng.choice(remaining)))
  350. continue
  352. p1 = tournament_select(pop, ranks, crowds, rng)
  353. p2 = tournament_select(pop, ranks, crowds, rng)
  355. child_g = make_child(p1, p2, rng, p_c=p_c, p_m=p_m)
  356. child_idx = canonicalize_to_index(child_g)
  357. if child_idx is None:
  358. continue
  359. child_idx = int(child_idx)
  361. if (child_idx in evaluated) or (child_idx in offspring):
  362. continue
  363. offspring.append(child_idx)
  365. for x in offspring:
  366. evaluated.add(int(x))
  368. # elitist replacement
  369. combined = pop + offspring
  370. combined_objs = df.loc[combined, obj_cols].to_numpy(dtype=float)
  371. fronts_R = fast_non_dominated_sort(combined, combined_objs)
  373. next_pop: List[int] = []
  374. for front_pos in fronts_R:
  375. if len(next_pop) + len(front_pos) <= P:
  376. next_pop.extend([int(combined[p]) for p in front_pos])
  377. else:
  378. cd = crowding_distance(front_pos, combined_objs)
  379. sorted_front = sorted(front_pos, key=lambda p: cd.get(p, 0.0), reverse=True)
  380. needed = P - len(next_pop)
  381. next_pop.extend([int(combined[p]) for p in sorted_front[:needed]])
  382. break
  384. pop = next_pop
  386. history.append({
  387. "gen": gen,
  388. "evaluated_idx": sorted(evaluated),
  389. "pareto_idx": current_pareto_in_evaluated(evaluated),
  390. "true_pareto_found": true_pareto_found_in_evaluated(evaluated),
  391. })
  393. return {
  394. "seed": seed,
  395. "P": P,
  396. "G": G,
  397. "history": history,
  398. "true_pareto_idx": list(map(int, true_pareto_idx)),
  399. }
  401. # %% [markdown]
  402. # ## (1) Run until generation 10 and plot the Pareto front at generation 10
  404. # %%
  405. from pathlib import Path
  406. import matplotlib.pyplot as plt
  408. G = 10
  409. seed = 0
  410. P = 24
  412. res = nsga2_run_generations(G=G, P=P, p_c=0.9, p_m=0.2, seed=seed)
  413. hG = res["history"][-1]
  414. true_pareto_idx = res["true_pareto_idx"]
  416. # output folder
  417. FIG_DIR = Path("figures")
  418. FIG_DIR.mkdir(exist_ok=True)
  420. # --- plot ---
  421. fig, ax = plt.subplots()
  423. ax.scatter(df["rela_error"], df["training_time"], alpha=0.25) # all 708
  424. tp = df.loc[true_pareto_idx]
  425. ax.scatter(tp["rela_error"], tp["training_time"], alpha=0.9) # ground-truth Pareto
  426. ev = df.loc[hG["evaluated_idx"]]
  427. ax.scatter(ev["rela_error"], ev["training_time"], alpha=0.9) # evaluated
  428. pr = df.loc[hG["pareto_idx"]]
  429. ax.scatter(pr["rela_error"], pr["training_time"], alpha=0.9) # Pareto in evaluated
  431. ax.set_xlabel("relative l2 error",fontsize=16)
  432. ax.set_ylabel("training time",fontsize=16)
  433. ax.set_title(f"NSGA-II Pareto front at generation {G} (seed={seed})")
  435. # --- save (PNG + PDF) ---
  436. png_path = FIG_DIR / f"nsga2_pareto_gen{G}_seed{seed}_P{P}.png"
  437. pdf_path = FIG_DIR / f"nsga2_pareto_gen{G}_seed{seed}_P{P}.pdf"
  438. fig.savefig(png_path, dpi=300, bbox_inches="tight")
  439. fig.savefig(pdf_path, bbox_inches="tight")
  440. print(f"Saved: {png_path.resolve()}")
  441. print(f"Saved: {pdf_path.resolve()}")
  443. plt.show()
  444. plt.close(fig)
  446. print(f"Generation {G}: evaluated = {len(hG['evaluated_idx'])}, "
  447. f"Pareto-in-evaluated size = {len(hG['pareto_idx'])}, "
  448. f"true Pareto found = {hG['true_pareto_found']} / {len(true_pareto_idx)}")
  451. # %% [markdown]
  452. # ## (2) 20 seeds: plot discovered ground-truth Pareto count vs generations (mean + 90% band)
  454. # %%
  455. from pathlib import Path
  456. import matplotlib.pyplot as plt
  458. n_runs = 20
  459. G = 20
  460. P = 24
  462. counts = np.zeros((n_runs, G + 1), dtype=float) # gen 0..G
  464. for s in range(n_runs):
  465. rr = nsga2_run_generations(G=G, P=P, p_c=0.9, p_m=0.2, seed=s)
  466. counts[s, :] = [hh["true_pareto_found"] for hh in rr["history"]]
  468. gens = np.arange(G + 1)
  469. mean = counts.mean(axis=0)
  470. low, high = np.percentile(counts, [5, 95], axis=0) # 90% band
  472. # output folder
  473. FIG_DIR = Path("figures")
  474. FIG_DIR.mkdir(exist_ok=True)
  476. # --- plot ---
  477. fig, ax = plt.subplots()
  478. ax.plot(gens, mean, label="mean")
  479. ax.fill_between(gens, low, high, alpha=0.25, label="90% band (5-95%)")
  480. ax.set_xlabel("generation",fontsize=16)
  481. ax.set_ylabel("# ground-truth Pareto architectures",fontsize=16)
  482. ax.set_title(f"NSGA-II (P={P}), {n_runs} seeds: discovery vs generation")
  483. ax.legend()
  485. # --- save (PNG + PDF) ---
  486. png_path = FIG_DIR / f"nsga2_true_pareto_discovery_mean90_G{G}_P{P}_runs{n_runs}.png"
  487. pdf_path = FIG_DIR / f"nsga2_true_pareto_discovery_mean90_G{G}_P{P}_runs{n_runs}.pdf"
  488. fig.savefig(png_path, dpi=300, bbox_inches="tight")
  489. fig.savefig(pdf_path, bbox_inches="tight")
  490. print(f"Saved: {png_path.resolve()}")
  491. print(f"Saved: {pdf_path.resolve()}")
  493. plt.show()
  494. plt.close(fig)
  497. # %%

nsga2_glucose_generations.ipynb at commit f07a6b7, no license · at the source

Overview

Authors: Qianying Cao1, Shanqing Liu1, Alan John Varghese2, Jérôme Darbon1, Michael S Triantafyllou3, George Em Karniadakis1
ORCID iDs: Qianying Cao, George Em Karniadakis
  1. Division of Applied Mathematics, Brown University, Providence, RI USA
  2. School of Engineering, Brown University, Providence, RI USA
  3. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA USA
Institutions: Brown University (United States); Massachusetts Institute of Technology (United States)
Journal: Nature communications, volume 17, issue 1, article 7058
Dates: received 19 June 2025; accepted 15 May 2026; published online 2 June 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41467-026-73687-9 · PMID 42230615 · PMCID PMC13392406 · OpenAlex W4406745912
Open access: gold, a free copy (OpenAlex)
Preprint: arxiv:2501.12215
Status: code verified
Categories: methods / tools (subfield)
Methods: Connectivity, Machine learning
Keywords: Computer science, Applied mathematics
Topic: Neural Networks and Applications (Artificial Intelligence, Computer Science), according to OpenAlex
Funding: United States Department of Defense | Defense Advanced Research Projects Agency (DARPA) (HR00112490484)
Citations: cited by 1 paper (Europe PMC); 69 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repository

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qianyingcao/Selection_Architecture_MOO

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: f07a6b72d93b8e04fcc8a7e564078d0743f7f763, 23 April 2026
Languages: Python (40), Jupyter (1)
Size: 44 files, 41 scripts
Software Heritage: not archived
Found in: “Code availability”
Holds: README, environment (requirements.txt), 1 notebook
Not found: license file, CITATION.cff, tests, continuous integration, documentation
Tools: PyTorch (37 files), NumPy (35 files), SciPy (31 files), Matplotlib (5 files), pandas (3 files)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
42 files
At the source: github.com/qianyingcao/Selection_Architecture_MOO

Code availability statement

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Read it in the paper: doi.org/10.1038/s41467-026-73687-9.

Tracing map

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What the map holds:

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  • 41 scripts, each with its path and the digest of its content;
  • 6 matches between paragraphs of the paper and lines of the code (method lexical-v1);
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Data

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Data availability statement

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Read it in the paper: doi.org/10.1038/s41467-026-73687-9.

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 6 authors, 2 keywords, 1 funder, 17 references.

Cite

This paper

Cao, Q., Liu, S., Varghese, A. J., Darbon, J., Triantafyllou, M. S., & Karniadakis, G. E. (2026). Automatic selection of the best neural architecture for time series forecasting. Nature communications, 17(1), 7058. https://doi.org/10.1038/s41467-026-73687-9

BibTeX

@article{cao2026automatic,
author = {Cao, Qianying and Liu, Shanqing and Varghese, Alan John and Darbon, Jérôme and Triantafyllou, Michael S and Karniadakis, George Em},
title = {{Automatic selection of the best neural architecture for time series forecasting}},
journal = {Nature communications},
year = {2026},
month = jun,
volume = {17},
number = {1},
pages = {7058},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/s41467-026-73687-9},
url = {https://doi.org/10.1038/s41467-026-73687-9},
pmid = {42230615},
pmcid = {PMC13392406}
}

RIS

TY - JOUR
AU - Cao, Qianying
AU - Liu, Shanqing
AU - Varghese, Alan John
AU - Darbon, Jérôme
AU - Triantafyllou, Michael S
AU - Karniadakis, George Em
TI - Automatic selection of the best neural architecture for time series forecasting
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/06/02
VL - 17
IS - 1
SP - 7058
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/s41467-026-73687-9
UR - https://doi.org/10.1038/s41467-026-73687-9
LA - en
ER -

CSL-JSON

{
"id": "10.1038/s41467-026-73687-9",
"type": "article-journal",
"title": "Automatic selection of the best neural architecture for time series forecasting",
"container-title": "Nature communications",
"author": [
{
"family": "Cao",
"given": "Qianying"
},
{
"family": "Liu",
"given": "Shanqing"
},
{
"family": "Varghese",
"given": "Alan John"
},
{
"family": "Darbon",
"given": "Jérôme"
},
{
"family": "Triantafyllou",
"given": "Michael S"
},
{
"family": "Karniadakis",
"given": "George Em"
}
],
"container-title-short": "Nat Commun",
"volume": "17",
"issue": "1",
"page": "7058",
"DOI": "10.1038/s41467-026-73687-9",
"PMID": "42230615",
"PMCID": "PMC13392406",
"ISSN": "2041-1723",
"publisher": "Nature Publishing Group",
"URL": "https://doi.org/10.1038/s41467-026-73687-9",
"language": "en",
"issued": {
"date-parts": [
[
2026,
6,
2
]
]
}
}

The tracing map gets a citation of its own once an author has validated it and it has a DOI.

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