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Added LinearODE

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AoranWANGRalf 2025-06-16 10:31:52 +08:00
parent d47b4efa33
commit 6a87ef96bf
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77
examples/pipelines/puzzle_configs/linearODE_test.json Normal file
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[
{
"k_range": [
0.15,
0.9
],
"x0_range": [
0.6,
1.8
],
"t_span": [
0,
6
],
"n_points": 60
},
{
"k_range": [
0.3,
2.0
],
"x0_range": [
0.7,
3.0
],
"t_span": [
0,
12
],
"n_points": 110
},
{
"k_range": [
0.05,
0.4
],
"x0_range": [
0.2,
1.3
],
"t_span": [
0,
8
],
"n_points": 80
},
{
"k_range": [
0.25,
1.2
],
"x0_range": [
0.4,
2.2
],
"t_span": [
0,
4
],
"n_points": 70
},
{
"k_range": [
0.2,
1.1
],
"x0_range": [
0.3,
2.5
],
"t_span": [
0,
9
],
"n_points": 90
}
]

152
examples/pipelines/puzzle_configs/linearODE_train.json Normal file
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[
{
"k_range": [
0.1,
1.0
],
"x0_range": [
0.5,
2.0
],
"t_span": [
0,
5
],
"n_points": 50
},
{
"k_range": [
0.2,
1.5
],
"x0_range": [
0.3,
2.5
],
"t_span": [
0,
10
],
"n_points": 100
},
{
"k_range": [
0.05,
0.5
],
"x0_range": [
0.4,
1.5
],
"t_span": [
0,
7
],
"n_points": 75
},
{
"k_range": [
0.1,
0.8
],
"x0_range": [
0.6,
2.0
],
"t_span": [
0,
3
],
"n_points": 40
},
{
"k_range": [
0.3,
1.2
],
"x0_range": [
0.5,
3.0
],
"t_span": [
0,
15
],
"n_points": 120
},
{
"k_range": [
0.2,
0.8
],
"x0_range": [
0.7,
2.5
],
"t_span": [
0,
6
],
"n_points": 55
},
{
"k_range": [
0.5,
1.8
],
"x0_range": [
0.4,
3.0
],
"t_span": [
0,
8
],
"n_points": 90
},
{
"k_range": [
0.1,
0.6
],
"x0_range": [
0.3,
1.8
],
"t_span": [
0,
4
],
"n_points": 60
},
{
"k_range": [
0.15,
1.0
],
"x0_range": [
0.5,
2.3
],
"t_span": [
0,
5
],
"n_points": 70
},
{
"k_range": [
0.3,
1.5
],
"x0_range": [
0.6,
2.8
],
"t_span": [
0,
10
],
"n_points": 120
}
]

78
internbootcamp/bootcamp/linearODE/linearODE.py Normal file
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import re
import json
import numpy as np
from scipy.integrate import odeint
from internbootcamp.bootcamp.base import Basebootcamp
class LinearODEBootcamp(Basebootcamp):
def __init__(
self,
k_range=(0.1, 1.0),
x0_range=(0.5, 2.0),
t_span=(0, 5),
n_points=50,
seed=None
):
self.k_range, self.x0_range = k_range, x0_range
self.t0, self.t1 = t_span
self.n_points = n_points
if seed is not None:
np.random.seed(seed)
def case_generator(self):
# 1. 随机采样参数 k 和初始值 x0
k = float(np.random.uniform(*self.k_range))
x0 = float(np.random.uniform(*self.x0_range))
# 2. 构造时间序列并模拟 dx/dt = -k * x
t = np.linspace(self.t0, self.t1, self.n_points).tolist()
def model(x, t_val):
return -k * x
x = odeint(model, x0, t).flatten().tolist()
return {"t": t, "x": x, "k": k}
def prompt_func(self, identity) -> str:
# 将 (t, x) 对格式化为提示
points = ", ".join(f"({t:.2f}, {x:.2f})"
for t, x in zip(identity["t"], identity["x"]))
return (
f"下面给出变量 x(t) 的观测数据点：\n{points}\n\n"
"请找出其满足的微分方程，形式为：dx/dt = f(x)。\n"
"只需返回 “dx/dt = <表达式>”。"
)
@staticmethod
def extract_output(output: str) -> str:
# 用正则提取“dx/dt = …”右侧的表达式
m = re.search(r"dx/dt\s*=\s*([^\n\r]+)", output)
return m.group(1).strip() if m else None
@classmethod
def _verify_correction(cls, solution: str, identity: dict) -> bool:
# 解析 LLM 给出的系数 c，形如 “c*x”
sol = solution.replace(" ", "")
match = re.fullmatch(r"([\-0-9\.eE]+)\*x", sol)
if not match:
return False
c = float(match.group(1))
# 验证 c ≈ -k
return abs(c + identity["k"]) < 1e-2
if __name__ == "__main__":
bootcamp = LinearODEBootcamp(seed=123)
# 生成几个样例
examples = [bootcamp.case_generator() for _ in range(3)]
for identity in examples:
# 构造“模型”返回答案，模拟 LLM 的输出
coeff = -identity["k"]
sol = f"{coeff:.4f}*x"
# 调用 Basebootcamp 提供的 verify_score 接口进行验证
score = bootcamp.verify_score(sol, identity, short_threshold=1e-2)
# 打印结果
print(json.dumps({
"identity": identity,
"solution": sol,
"verify_score": score
}, ensure_ascii=False, indent=2))