相关实验视频
Updated: Jun 9, 2025

13:19
Deep Neural Networks for Image-Based Dietary Assessment
Published on: March 13, 2021
9.0K
通过深度神经网络,通过巴纳赫值,高维函数的近最佳学习
Ben Adcock1, Simone Brugiapaglia2, Nick Dexter3
1Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby BC, Canada, V5A 1S6.
概括
深度学习 (DL) 对科学计算有希望,但缺乏对数值分析的理解. 本研究为深度神经网络 (DNN) 建立定理,以近似参数部分微分方程 (PDE),克服数据稀缺性和高维度.
科学领域:
- 计算科学与工程 (CSE)
- 数字分析 数字分析
- 深度学习 (DL) 是指深度学习.
背景情况:
- 深度学习 (DL) 在计算科学与工程 (CSE) 中越来越多地应用,显示了革命性的科学计算的前景.
- 然而,DL的可靠性和效率,特别是关于稳定性,稳定性,准确性和样本复杂性等数值分析方面,仍然不明确.
- 对参数部分微分方程 (PDEs) 的近似解决方案对于CSE的不确定性量化 (UQ) 是至关重要的,但通常涉及稀缺,易出错的数据和无限维函数空间.
研究的目的:
- 为使用深度神经网络 (DNN) 提供理论论证,以近似解决参数PDE的解决方案,解决维度的诅咒.
- 为DNN建立实际存在定理,克服数据稀缺性和高维度在近似复杂函数中的局限性.
- 开发一个理论框架,用于高维近CSE的非侵入性方法.
主要方法:
- 为具有维度独立架构的DNN建立存在定理.
- 开发培训程序,以尽量减少规范化的l2-loss.
- 扩展巴纳赫值向量的压缩传感和使用DNN的多项式仿真.
主要成果:
- 证明DNN可以克服尺寸性的诅咒,以近似参数 PDE 解决方案.
- 在训练数据量 (m) 方面实现近最佳的代数收率.
- 从粗数据中计算高准确度DNN近似中的所有错误来源 (采样,优化,近似,离散).
结论:
- 深度神经网络 (DNN) 为计算科学和工程中的高维近似提供了理论上合理的,非侵入性的方法.
- 开发的方法为古典技术提供了可行的替代方案,特别是在处理稀缺数据和复杂的高维问题时.
- 这项工作弥合了DL应用和严格的数值分析之间的差距,提高了DL在科学计算中的可靠性和适用性.
相关概念视频
Associative Learning
300
Associative learning is a fundamental concept in behavioral psychology, wherein a connection is established between two stimuli or events, leading to a learned response. This process is critical in understanding how behaviors are acquired and modified. Conditioning, the mechanism through which associations are formed, can be divided into two main types: classical conditioning and operant conditioning, each elucidating different aspects of associative learning.
Classical conditioning, also known...
Classical conditioning, also known...
300
Multi-input and Multi-variable systems
100
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence...
In the absence...
100
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
42
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
42
Neural Circuits
1.1K
Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
1.1K
Functional Classification of Joints
3.8K
Functional Classification of Joints
The functional classification of joints is determined by the amount of mobility between the adjacent bones. Joints are functionally classified as a synarthrosis or immobile joint, an amphiarthrosis or slightly moveable joint, or as a diarthrosis, a freely moveable joint. Fibrous and cartilaginous joints can be functionally classified as either synarthroses or amphiarthroses, whereas all synovial joints are classified as diarthroses.
Synarthrosis
An...
The functional classification of joints is determined by the amount of mobility between the adjacent bones. Joints are functionally classified as a synarthrosis or immobile joint, an amphiarthrosis or slightly moveable joint, or as a diarthrosis, a freely moveable joint. Fibrous and cartilaginous joints can be functionally classified as either synarthroses or amphiarthroses, whereas all synovial joints are classified as diarthroses.
Synarthrosis
An...
3.8K

