# Physics-Driven ML-Based Modelling for Correcting Inverse Estimation

arXiv: https://arxiv.org/abs/2309.13985 · HTML: https://mlsanity.com/paper/2309.13985/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 78 references that are in the map.
- First posted on arXiv 25 Sep 2023.

## Builds on (most cited first, 25 of 25)

- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Self-Supervised Exploration via Disagreement](https://mlsanity.com/paper/1906.04161/) (2019)
- [Optimization of Molecules via Deep Reinforcement Learning](https://mlsanity.com/paper/1810.08678/) (2018)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Model-Based Active Exploration](https://mlsanity.com/paper/1810.12162/) (2018)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Model Inversion Networks for Model-Based Optimization](https://mlsanity.com/paper/1912.13464/) (2019)
- [On Learning to Think: Algorithmic Information Theory for Novel Combinations of Reinforcement Learning Controllers and Recurrent Neural World Models](https://mlsanity.com/paper/1511.09249/) (2015)
- [RoMA: Robust Model Adaptation for Offline Model-based Optimization](https://mlsanity.com/paper/2110.14188/) (2021)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation](https://mlsanity.com/paper/2102.07970/) (2021)
- [Direct shape optimization through deep reinforcement learning](https://mlsanity.com/paper/1908.09885/) (2019)
- [Deep Neural Network Ensembles against Deception: Ensemble Diversity, Accuracy and Robustness](https://mlsanity.com/paper/1908.11091/) (2019)
- [TiCo: Transformation Invariance and Covariance Contrast for Self-Supervised Visual Representation Learning](https://mlsanity.com/paper/2206.10698/) (2022)
- [Runtime Safety Assurance for Learning-enabled Control of Autonomous Driving Vehicles](https://mlsanity.com/paper/2109.13446/) (2021)
- [A General Framework Combining Generative Adversarial Networks and Mixture Density Networks for Inverse Modeling in Microstructural Materials Design](https://mlsanity.com/paper/2101.10553/) (2021)
- [Neural Optimization Machine: A Neural Network Approach for Optimization](https://mlsanity.com/paper/2208.03897/) (2022)
- [A Deep Reinforcement Learning Approach for Dynamically Stable Inverse Kinematics of Humanoid Robots](https://mlsanity.com/paper/1801.10425/) (2018)
- [Global Optimization Networks](https://mlsanity.com/paper/2202.01277/) (2022)
- [Self-Validated Physics-Embedding Network: A General Framework for Inverse Modelling](https://mlsanity.com/paper/2210.06071/) (2022)

## Built on by (most cited first, 1 of 1)

- [CILF-CIAE: CLIP-driven Image-Language Fusion for Correcting Inverse Age Estimation](https://mlsanity.com/paper/2312.01758/) (2023)

## Abstract (arXiv)

When deploying machine learning estimators in science and engineering (SAE) domains, it is critical to avoid failed estimations that can have disastrous consequences, e.g., in aero engine design. This work focuses on detecting and correcting failed state estimations before adopting them in SAE inverse problems, by utilizing simulations and performance metrics guided by physical laws. We suggest to flag a machine learning estimation when its physical model error exceeds a feasible threshold, and propose a novel approach, GEESE, to correct it through optimization, aiming at delivering both low error and high efficiency. The key designs of GEESE include (1) a hybrid surrogate error model to provide fast error estimations to reduce simulation cost and to enable gradient based backpropagation of error feedback, and (2) two generative models to approximate the probability distributions of the candidate states for simulating the exploitation and exploration behaviours. All three models are constructed as neural networks. GEESE is tested on three real-world SAE inverse problems and compared to a number of state-of-the-art optimization/search approaches. Results show that it fails the least number of times in terms of finding a feasible state correction, and requires physical evaluations less frequently in general.