贝叶斯反向问题与有条件的Sinkhorn生成对抗网络在最小体积的潜空间
Qiuyi Chen1, Panagiotis Tsilifis2, Mark Fuge3
1Center for Risk and Reliability, Department of Mechanical Engineering, University of Maryland, College Park, 20742, MD, USA; Artificial Intelligence Group, General Electric Vernova Advanced Research, One Research Circle, Niskayuna, 12309, NY, USA.
概括
本研究介绍了Least Volume,这是一种用于非线性维度减小的新方法,用于改善复杂反向问题的生成模型. 这种方法可以有效地训练潜伏条件GAN,以便在高维科学和工程应用中进行准确的贝叶斯推理.
科学领域:
- 科学计算科学计算
- 数据科学数据科学数据科学
- 应用数学 应用数学 应用数学
背景情况:
- 科学和工程中的反向问题由于高维度,非线性和模型不确定性而具有挑战性.
- 生成对立网络 (GAN) 对贝叶斯反向问题有前途,但与复杂的高维数据集扎.
研究的目的:
- 解决当前方法在解决高维和非线性反向问题的局限性.
- 引入一种新的无监督非线性维度缩小技术,以改善生成模型培训.
主要方法:
- 最小体积:一种无监督的非线性维度缩小方法,用于识别内在数据维度,并学习最小隐性变量表示.
- 潜伏条件GAN框架:在已识别的低维潜伏空间中实现生成模型的高效和准确的训练,用于后置推理.
主要成果:
- 证明了最小体积方法的成功应用,用于复杂的反向问题的缩小维度.
- 实现了条件生成模型的高效准确训练,从而形成了一个强大的潜在条件GAN框架.
- 在各种应用上验证了该方法,包括ODE中的参数反转和地下流量问题.
结论:
- 最小卷有效地解决了反向问题的高维度和非线性,提高了生成模型的性能.
- 拟议的潜在条件GAN框架为复杂的科学和工程领域的贝叶斯后置推理提供了一个强大的工具.
- 可观测和不可观测的内在维度显著影响反向问题的解决方案.
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