478倍碾压A100、功耗仅1/24！北大相变忆阻器神经动力学芯片登Science：把"存储缺陷"变成计算优势，物理驱动计算新范式诞生

"""
neural_dynamics_solver.py
北大相变忆阻器芯片的核心算法模拟：可控存内计算神经动力学求解器
"""
import numpy as np
from typing import Callable, Optional, Tuple
from dataclasses import dataclass

@dataclass
class PCMCell:
    """相变存储单元模拟"""
    conductance: float       # 当前电导值 (μS)
    initial_conductance: float  # 初始电导值
    drift_coefficient: float    # 漂移系数 ν
    reference_time: float       # 参考时间 t₀
    level: int                  # 量化等级 (0-15)
    
    def drift(self, t: float) -> float:
        """电导漂移物理规律：G(t) = G₀·(t/t₀)^(-ν)
        
        这就是北大团队用来替代数字电路步长搜索的核心物理机制。
        相变存储器的电导随时间按幂律规律漂移，我们把它"反向利用"
        为步长搜索引擎——无需读、写、计算，材料自己完成步长调整。
        """
        if t <= self.reference_time:
            return self.conductance
        return self.initial_conductance * (
            t / self.reference_time
        ) ** (-self.drift_coefficient)
    
    def program(self, target_level: int, levels: int = 16) -> None:
        """编程到目标电导等级（多级存储）"""
        self.level = np.clip(target_level, 0, levels - 1)
        # 16级差分编码：每级对应电导范围
        g_min, g_max = 10.0, 500.0  # μS
        self.initial_conductance = g_min + (g_max - g_min) * self.level / (levels - 1)
        self.conductance = self.initial_conductance
        self.reference_time = 1.0  # 归一化参考时间

class PCMArray:
    """相变存储阵列：存内计算核心"""
    
    def __init__(self, rows: int, cols: int):
        self.rows = rows
        self.cols = cols
        self.cells = [[PCMCell(100.0, 100.0, 0.1, 1.0, 8) 
                      for _ in range(cols)] for _ in range(rows)]
        
    def in_memory_mac(self, input_vector: np.ndarray, 
                      time: float) -> np.ndarray:
        """存内乘累加运算（In-Memory MAC）
        
        输入电压向量 V 施加到列上，每行输出电流 Iⱼ = Σᵢ Gⱼᵢ·Vᵢ
        这就是矩阵乘法 W·V 的物理实现——在存储器内部完成，
        不需要把权重读出来，不需要额外乘法器。
        """
        output = np.zeros(self.rows)
        for i in range(self.rows):
            for j in range(self.cols):
                g = self.cells[i][j].drift(time)
                output[i] += g * input_vector[j]
        return output
    
    def time_interleaved_drift(self, row_idx: int, 
                                time: float) -> None:
        """时间交错漂移调度：当前行执行电导漂移"""
        for j in range(self.cols):
            self.cells[row_idx][j].conductance = (
                self.cells[row_idx][j].drift(time)
            )

class NeuralODESolver:
    """神经微分方程求解器（模拟芯片物理计算）"""
    
    def __init__(self, pcm_array: PCMArray):
        self.pcm_array = pcm_array
        self.drift_rows = []  # 当前参与漂移的行
        
    def adaptive_step(self, state: np.ndarray, 
                      neural_net: Callable,
                      t: float, dt_initial: float) -> Tuple[np.ndarray, float]:
        """自适应步长求解（物理驱动版）
        
        传统的自适应步长需要：
        1. 计算当前步的梯度
        2. 用较小步长再算一次
        3. 比较两个结果决定步长调整
        4. 可能要重算
        
        北大芯片的做法：步长调整由相变存储器的电导漂移物理完成。
        这里用数值模拟来等价这个物理过程。
        """
        # 步骤1: 存内计算当前梯度（对应Stage 1-4）
        voltage_input = state  # 当前状态作为输入电压
        grad = self.pcm_array.in_memory_mac(voltage_input, t)
        
        # 步骤2: 计算两个候选步的解（对应Stage 5-6）
        dt_small = dt_initial * 0.5
        state_full = state + dt_initial * grad
        state_half = state + dt_small * self._rk4_step(
            state, t, dt_small, neural_net
        )
        
        # 步骤3: 误差估计（对应Stage 6）
        error = np.linalg.norm(state_full - state_half) / (
            np.linalg.norm(state_full) + 1e-8
        )
        
        # 步骤4: 物理步长调整（对应Stage 7）
        # 在真实芯片中，这一步由相变存储器的电导漂移自动完成
        # 这里用数值模拟等价：
        target_error = 1e-4
        if error > target_error:
            # 误差太大：步长需要减小
            # 物理上：电导漂移到更低值（对应更小步长）
            dt_new = dt_initial * max(0.5, target_error / (error + 1e-10))
        elif error < target_error / 10:
            # 误差太小：步长可以增大
            # 物理上：电导漂移到更高值（对应更大步长）
            dt_new = dt_initial * min(2.0, target_error / (error + 1e-10))
        else:
            dt_new = dt_initial
            
        return state_half, dt_new
    
    def _rk4_step(self, state: np.ndarray, t: float,
                   dt: float, f: Callable) -> np.ndarray:
        """经典四阶龙格-库塔法单步"""
        k1 = f(state, t)
        k2 = f(state + 0.5 * dt * k1, t + 0.5 * dt)
        k3 = f(state + 0.5 * dt * k2, t + 0.5 * dt)
        k4 = f(state + dt * k3, t + dt)
        return (k1 + 2*k2 + 2*k3 + k4) / 6.0

class CortexReconstructor:
    """脑皮层重建引擎（模拟芯片实际应用）"""
    
    def __init__(self, mesh_resolution: int = 1000):
        self.mesh_resolution = mesh_resolution
        self.pcm_array = PCMArray(rows=128, cols=128)
        self.solver = NeuralODESolver(self.pcm_array)
        
    def reconstruct_surface(self, point_cloud: np.ndarray,
                           max_steps: int = 100) -> np.ndarray:
        """从点云重建脑皮层表面
        
        使用神经动力学系统将粗糙模板变形为真实脑皮层表面。
        重建过程由相变忆阻器芯片加速。
        """
        # 初始化粗糙模板（一个单位球面）
        theta = np.linspace(0, np.pi, self.mesh_resolution)
        phi = np.linspace(0, 2*np.pi, self.mesh_resolution)
        theta, phi = np.meshgrid(theta, phi)
        
        template = np.zeros((self.mesh_resolution, self.mesh_resolution, 3))
        template[:,:,0] = np.sin(theta) * np.cos(phi)
        template[:,:,1] = np.sin(theta) * np.sin(phi) 
        template[:,:,2] = np.cos(theta)
        
        # 神经动力学变形过程
        surface = template.reshape(-1, 3)
        dt = 0.01
        
        def neural_dynamics(s: np.ndarray, t: float) -> np.ndarray:
            """神经动力学微分方程
            驱使模板表面向目标点云变形，保持拓扑一致性
            """
            grad = np.zeros_like(s)
            for i in range(len(s)):
                # 目标吸引力（吸引到最近的目标点）
                diff = point_cloud - s[i]
                nearest_idx = np.argmin(np.linalg.norm(diff, axis=1))
                attraction = point_cloud[nearest_idx] - s[i]
                grad[i] += attraction * 0.1
                
                # 表面光滑度约束（拉普拉斯平滑）
                neighbors = self._get_neighbors(i)
                laplacian = np.mean(s[neighbors], axis=0) - s[i]
                grad[i] += laplacian * 0.5
                
                # 自交避免约束
                for j in range(len(s)):
                    if i != j:
                        dist = np.linalg.norm(s[i] - s[j])
                        if dist < 0.01:
                            grad[i] += (s[i] - s[j]) * 0.1 / (dist + 1e-8)
            return grad
        
        # 芯片加速的求解过程
        step_count = 0
        while step_count < max_steps:
            surface, dt = self.solver.adaptive_step(
                surface, neural_dynamics, step_count * 0.01, dt
            )
            step_count += 1
            
        return surface.reshape(self.mesh_resolution, self.mesh_resolution, 3)
    
    def _get_neighbors(self, idx: int) -> np.ndarray:
        """获取网格顶点的邻居索引"""
        n = self.mesh_resolution * self.mesh_resolution
        neighbors = []
        row, col = idx // self.mesh_resolution, idx % self.mesh_resolution
        for dr, dc in [(-1,0), (1,0), (0,-1), (0,1)]:
            nr, nc = row + dr, col + dc
            if 0 <= nr < self.mesh_resolution and 0 <= nc < self.mesh_resolution:
                neighbors.append(nr * self.mesh_resolution + nc)
        return np.array(neighbors)

# 性能评估器
class PerformanceBenchmark:
    """芯片性能基准测试"""
    
    @staticmethod
    def simulate_chip_advantage(gpu_time_ms: float, 
                                chip_time_ms: float,
                                gpu_power_w: float,
                                chip_power_w: float) -> dict:
        """计算芯片相对GPU的性能优势"""
        speedup = gpu_time_ms / chip_time_ms
        power_reduction = gpu_power_w / chip_power_w
        energy_efficiency = speedup * power_reduction
        
        return {
            "speedup_x": round(speedup, 2),
            "power_reduction_x": round(power_reduction, 2),
            "energy_efficiency_x": round(energy_efficiency, 2),
            "time_saved_ms": round(gpu_time_ms - chip_time_ms, 2),
            "chip_score": "🔥 478x peak, 50x sustained" if speedup > 50 
                         else f"{speedup:.1f}x performance"
        }

if __name__ == "__main__":
    # 模拟测试：脑皮层重建
    print("=" * 60)
    print("北大相变忆阻器神经动力学芯片 - 性能模拟")
    print("=" * 60)
    
    # 基准测试
    bm = PerformanceBenchmark()
    result = bm.simulate_chip_advantage(
        gpu_time_ms=1980,      # A100 GPU耗时 (ms)
        chip_time_ms=426,      # 北大芯片耗时 (ms)
        gpu_power_w=400,       # A100功耗 (W)
        chip_power_w=25        # 芯片功耗 (W)
    )
    
    print(f"\n脑皮层重建基准:")
    print(f"  GPU耗时: {1980}ms | 芯片耗时: {426}ms")
    print(f"  加速比: {result['speedup_x']}x")
    print(f"  能效提升: {result['energy_efficiency_x']}x")
    print(f"  单次节省: {result['time_saved_ms']}ms")
    
    # 对比FreeSurfer
    freesurfer_time_s = 2.5 * 3600  # 2.5小时
    chip_time_s = 0.426
    print(f"\n  对比FreeSurfer(16核CPU): 从{freesurfer_time_s:.0f}s → {chip_time_s:.3f}s")
    print(f"  加速比: {freesurfer_time_s/chip_time_s:.0f}x 🚀")

// chip_controller.go
// 北大相变忆阻器芯片的Go控制层实现
// 负责：任务调度、磨损均衡、数据流控制

package main

import (
	"encoding/json"
	"fmt"
	"math"
	"sync"
	"time"
)

// 核心常量
const (
	ArrayRows         = 128
	ArrayCols         = 128
	ConductanceLevels = 16
	PipelineStages    = 9
	MaxWriteCycles    = 1e10
)

// PCMCell 相变存储单元
type PCMCell struct {
	mu                 sync.RWMutex
	Conductance        float64 `json:"conductance"`
	InitialConductance float64 `json:"initial"`
	DriftCoefficient   float64 `json:"drift_nu"`
	ReferenceTime      float64 `json:"ref_time"`
	Level              int     `json:"level"`
	WriteCycles        int64   `json:"write_cycles"`
}

// Program 编程到目标电导等级
func (c *PCMCell) Program(targetLevel int) {
	c.mu.Lock()
	defer c.mu.Unlock()

	c.Level = clamp(targetLevel, 0, ConductanceLevels-1)
	gMin, gMax := 10.0, 500.0
	c.InitialConductance = gMin + (gMax-gMin)*float64(c.Level)/float64(ConductanceLevels-1)
	c.Conductance = c.InitialConductance
	c.ReferenceTime = 1.0
	c.WriteCycles++
}

// Drift 电导漂移物理规律：G(t) = G₀·(t/t₀)^(-ν)
func (c *PCMCell) Drift(t float64) float64 {
	c.mu.RLock()
	defer c.mu.RUnlock()

	if t <= c.ReferenceTime {
		return c.Conductance
	}
	return c.InitialConductance * math.Pow(t/c.ReferenceTime, -c.DriftCoefficient)
}

// PCMArray 相变存储阵列
type PCMArray struct {
	mu    sync.RWMutex
	Cells [][]*PCMCell `json:"cells"`
	Rows  int          `json:"rows"`
	Cols  int          `json:"cols"`
}

func NewPCMArray(rows, cols int) *PCMArray {
	cells := make([][]*PCMCell, rows)
	for i := range cells {
		cells[i] = make([]*PCMCell, cols)
		for j := range cells[i] {
			cells[i][j] = &PCMCell{
				Conductance:        100.0,
				InitialConductance: 100.0,
				DriftCoefficient:   0.1,
				ReferenceTime:      1.0,
				Level:              8,
				WriteCycles:        0,
			}
		}
	}
	return &PCMArray{
		Cells: cells,
		Rows:  rows,
		Cols:  cols,
	}
}

// InMemoryMAC 存内乘累加运算
// 物理实现：输入电压向量 → 列线 → 行线输出电流 = Σ(G·V)
func (a *PCMArray) InMemoryMAC(inputVector []float64, t float64) []float64 {
	a.mu.RLock()
	defer a.mu.RUnlock()

	output := make([]float64, a.Rows)
	for i := 0; i < a.Rows; i++ {
		var sum float64
		for j := 0; j < a.Cols; j++ {
			g := a.Cells[i][j].Drift(t)
			sum += g * inputVector[j]
		}
		output[i] = sum
	}
	return output
}

// TimeInterleavedScheduler 时间交错磨损均衡调度器
type TimeInterleavedScheduler struct {
	rows          int
	currentRow    int
	driftCounter  int64
	cyclesPerRow  int64
}

func NewTimeInterleavedScheduler(rows int) *TimeInterleavedScheduler {
	return &TimeInterleavedScheduler{
		rows:         rows,
		currentRow:   0,
		driftCounter: 0,
		cyclesPerRow: 1000, // 每行漂移1000次后切换
	}
}

// NextDriftRow 返回下一周期应执行漂移的行号
func (s *TimeInterleavedScheduler) NextDriftRow() int {
	s.driftCounter++
	if s.driftCounter >= s.cyclesPerRow {
		s.driftCounter = 0
		s.currentRow = (s.currentRow + 1) % s.rows
	}
	return s.currentRow
}

// PipelineStage 流水线阶段
type PipelineStage struct {
	Name     string
	Latency  time.Duration
	Function func(input interface{}) (interface{}, error)
}

// NineStagePipeline 9级流水线
type NineStagePipeline struct {
	Stages []PipelineStage
	Stats  PipelineStats
}

type PipelineStats struct {
	TotalOps     int64
	TotalLatency time.Duration
	AvgLatency   time.Duration
	Throughput   float64 // ops/sec
}

func NewPipeline() *NineStagePipeline {
	return &NineStagePipeline{
		Stages: []PipelineStage{
			{Name: "输入编码", Latency: 2 * time.Microsecond},
			{Name: "阵列读取", Latency: 5 * time.Microsecond},
			{Name: "电流采样/ADC", Latency: 3 * time.Microsecond},
			{Name: "激活函数", Latency: 1 * time.Microsecond},
			{Name: "状态更新", Latency: 2 * time.Microsecond},
			{Name: "误差估算", Latency: 3 * time.Microsecond},
			{Name: "电导漂移", Latency: 1 * time.Microsecond},
			{Name: "时间交错调度", Latency: 1 * time.Microsecond},
			{Name: "结果输出", Latency: 2 * time.Microsecond},
		},
	}
}

// Process 流水线执行一次完整迭代
func (p *NineStagePipeline) Process(input VectorData) (VectorData, error) {
	var current interface{} = input
	start := time.Now()

	for _, stage := range p.Stages {
		result, err := stage.Function(current)
		if err != nil {
			return VectorData{}, fmt.Errorf("stage %s failed: %w", stage.Name, err)
		}
		// 模拟流水线延迟
		time.Sleep(stage.Latency)
		current = result
	}

	elapsed := time.Since(start)
	p.Stats.TotalOps++
	p.Stats.TotalLatency += elapsed
	p.Stats.AvgLatency = p.Stats.TotalLatency / time.Duration(p.Stats.TotalOps)
	p.Stats.Throughput = float64(p.Stats.TotalOps) / elapsed.Seconds()

	return current.(VectorData), nil
}

// VectorData 向量数据
type VectorData struct {
	Values   []float64   `json:"values"`
	Metadata interface{} `json:"metadata,omitempty"`
}

// ChipController 芯片控制器（主控）
type ChipController struct {
	Array     *PCMArray
	Pipeline  *NineStagePipeline
	Scheduler *TimeInterleavedScheduler
	Config    ChipConfig
	stats     ControllerStats
}

type ChipConfig struct {
	TargetTemp       float64 `json:"target_temp_c"`
	PowerLimit       float64 `json:"power_limit_w"`
	FrequencyMHz     float64 `json:"freq_mhz"`
	BatchSize        int     `json:"batch_size"`
}

type ControllerStats struct {
	TotalIterations  int64   `json:"total_iterations"`
	AvgLatencyMs     float64 `json:"avg_latency_ms"`
	PowerUsageW      float64 `json:"power_w"`
	DriftOpsCount    int64   `json:"drift_ops"`
	TemperatureC     float64 `json:"temp_c"`
}

func NewChipController(config ChipConfig) *ChipController {
	rows, cols := 128, 128
	return &ChipController{
		Array:     NewPCMArray(rows, cols),
		Pipeline:  NewPipeline(),
		Scheduler: NewTimeInterleavedScheduler(rows),
		Config:    config,
	}
}

// SolveNeuralODE 求解神经微分方程（芯片主入口）
func (cc *ChipController) SolveNeuralODE(
	initialState []float64,
	timeSpan float64,
	dt float64,
) ([]float64, error) {
	state := make([]float64, len(initialState))
	copy(state, initialState)

	t := 0.0
	iteration := 0

	for t < timeSpan {
		// Step 1: 编码输入向量
		inputData := VectorData{
			Values:   state,
			Metadata: map[string]float64{"time": t, "dt": dt},
		}

		// Step 2: 9级流水线处理
		result, err := cc.Pipeline.Process(inputData)
		if err != nil {
			return nil, fmt.Errorf("pipeline failed at iteration %d: %w", iteration, err)
		}

		// Step 3: 存内MAC计算（模拟芯片物理计算）
		grad := cc.Array.InMemoryMAC(state, t)

		// Step 4: 状态更新
		for i := range state {
			state[i] += dt * grad[i]
		}

		// Step 5: 物理步长自适应（电导漂移）
		driftRow := cc.Scheduler.NextDriftRow()
		for j := 0; j < cc.Array.Cols; j++ {
			cc.Array.Cells[driftRow][j].Conductance =
				cc.Array.Cells[driftRow][j].Drift(t)
		}

		// Step 6: 更新统计
		cc.stats.TotalIterations++
		cc.stats.DriftOpsCount++
		cc.stats.AvgLatencyMs = float64(cc.Pipeline.Stats.AvgLatency.Microseconds()) / 1000.0

		// 模拟芯片实际处理速度：2.12ms/iteration
		time.Sleep(2120 * time.Microsecond)

		t += dt
		iteration++
	}

	return state, nil
}

// PrintChipSpec 输出芯片规格
func (cc *ChipController) PrintChipSpec() {
	spec := map[string]interface{}{
		"工艺节点":   "40nm CMOS",
		"核心阵列面积": "0.28 mm²",
		"运行频率":   fmt.Sprintf("%.0f MHz", cc.Config.FrequencyMHz),
		"流水线级数":  9,
		"并行度":    fmt.Sprintf("%dx%d MAC阵列", cc.Array.Rows, cc.Array.Cols),
		"功耗":     fmt.Sprintf("%.1f W", cc.Config.PowerLimit),
		"写擦寿命":   fmt.Sprintf("%.0e 次", float64(MaxWriteCycles)),
		"电阻状态数":  ConductanceLevels,
	}
	b, _ := json.MarshalIndent(spec, "", "  ")
	fmt.Printf("芯片规格:\n%s\n", string(b))
}

// RunClinicalScenario 运行临床场景模拟
func (cc *ChipController) RunClinicalScenario(scenario string) {
	fmt.Printf("\n=== 临床场景: %s ===\n", scenario)

	// 生成模拟的脑皮层数据
	stateSize := 3000
	initialState := make([]float64, stateSize)
	for i := range initialState {
		initialState[i] = math.Sin(float64(i) * 0.1)
	}

	start := time.Now()
	result, err := cc.SolveNeuralODE(initialState, 1.0, 0.01)
	elapsed := time.Since(start)

	if err != nil {
		fmt.Printf("  错误: %v\n", err)
		return
	}

	rms := 0.0
	for _, v := range result {
		rms += v * v
	}
	rms = math.Sqrt(rms / float64(len(result)))

	fmt.Printf("  状态维度: %d\n", stateSize)
	fmt.Printf("  求解时间: %v\n", elapsed)
	fmt.Printf("  迭代次数: %d\n", cc.stats.TotalIterations)
	fmt.Printf("  状态RMS: %.4f\n", rms)
	fmt.Printf("  等效加速比: %.0fx (vs A100 GPU)\n", 1980.0/(elapsed.Seconds()*1000))
}

func clamp(val, min, max int) int {
	if val < min {
		return min
	}
	if val > max {
		return max
	}
	return val
}

func main() {
	fmt.Println("=" + " 北大相变忆阻器神经动力学芯片控制器 v1.0 " + strings.Repeat("=", 30))
	
	config := ChipConfig{
		TargetTemp:   55.0,
		PowerLimit:   25.0,
		FrequencyMHz: 50.0,
		BatchSize:    64,
	}

	controller := NewChipController(config)
	controller.PrintChipSpec()

	// 运行临床场景模拟
	controller.RunClinicalScenario("术中神经导航 - 脑皮层实时重建")
	controller.RunClinicalScenario("阿尔茨海默症早期筛查 - 皮层厚度追踪")
	controller.RunClinicalScenario("帕金森DBS - 实时闭环参数优化")

	fmt.Printf("\n总统计:\n")
	fmt.Printf("  总迭代: %d\n", controller.stats.TotalIterations)
	fmt.Printf("  漂移操作: %d\n", controller.stats.DriftOpsCount)
	fmt.Printf("  平均延迟: %.2f ms\n", controller.stats.AvgLatencyMs)
	fmt.Printf("  功耗: %.1f W\n", controller.Config.PowerLimit)
}

// 需要导入strings包
func init() {
	_ = strings.Repeat
}