# SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates

arXiv: https://arxiv.org/abs/2008.10546 · HTML: https://mlsanity.com/paper/2008.10546/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2020.

## Built on by (most cited first, 30 of 75)

- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression](https://mlsanity.com/paper/2103.13629/) (2021)
- [Robust Calibration with Multi-domain Temperature Scaling](https://mlsanity.com/paper/2206.02757/) (2022)
- [Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations](https://mlsanity.com/paper/2102.06559/) (2021)
- [Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data](https://mlsanity.com/paper/2402.14989/) (2024)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [Climate Modeling with Neural Diffusion Equations](https://mlsanity.com/paper/2111.06011/) (2021)
- [End-to-End Stochastic Optimization with Energy-Based Model](https://mlsanity.com/paper/2211.13837/) (2022)
- [Policy Analysis using Synthetic Controls in Continuous-Time](https://mlsanity.com/paper/2102.01577/) (2021)
- [Sample Efficient Reinforcement Learning via Model-Ensemble Exploration and Exploitation](https://mlsanity.com/paper/2107.01825/) (2021)
- [Collaborative Uncertainty in Multi-Agent Trajectory Forecasting](https://mlsanity.com/paper/2110.13947/) (2021)
- [I Find Your Lack of Uncertainty in Computer Vision Disturbing](https://mlsanity.com/paper/2104.08188/) (2021)
- [When in Doubt: Neural Non-Parametric Uncertainty Quantification for Epidemic Forecasting](https://mlsanity.com/paper/2106.03904/) (2021)
- [Exploring Depth Contribution for Camouflaged Object Detection](https://mlsanity.com/paper/2106.13217/) (2021)
- [Neural network stochastic differential equation models with applications to financial data forecasting](https://mlsanity.com/paper/2111.13164/) (2021)
- [Collaborative Uncertainty Benefits Multi-Agent Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2207.05195/) (2022)
- [Improving Transferability for Cross-domain Trajectory Prediction via Neural Stochastic Differential Equation](https://mlsanity.com/paper/2312.15906/) (2023)
- [STUaNet: Understanding uncertainty in spatiotemporal collective human mobility](https://mlsanity.com/paper/2102.06027/) (2021)
- [Uncertainty-Aware Credit Card Fraud Detection Using Deep Learning](https://mlsanity.com/paper/2107.13508/) (2021)
- [How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equations](https://mlsanity.com/paper/2306.06335/) (2023)
- [Fractional SDE-Net: Generation of Time Series Data with Long-term Memory](https://mlsanity.com/paper/2201.05974/) (2022)
- [Variational Inference for SDEs Driven by Fractional Noise](https://mlsanity.com/paper/2310.12975/) (2023)
- [PGODE: Towards High-quality System Dynamics Modeling](https://mlsanity.com/paper/2311.06554/) (2023)
- [Uncertainty Quantification in Machine Learning for Biosignal Applications -- A Review](https://mlsanity.com/paper/2312.09454/) (2023)
- [Semantic Tube Prediction: Beating LLM Data Efficiency with JEPA](https://mlsanity.com/paper/2602.22617/) (2026)
- [Uncertainty and Structure in Neural Ordinary Differential Equations](https://mlsanity.com/paper/2305.13290/) (2023)
- [FedCal: Achieving Local and Global Calibration in Federated Learning via Aggregated Parameterized Scaler](https://mlsanity.com/paper/2405.15458/) (2024)
- [DutyTTE: Deciphering Uncertainty in Origin-Destination Travel Time Estimation](https://mlsanity.com/paper/2408.12809/) (2024)
- [Universal Approximation Theorem of Deep Q-Networks](https://mlsanity.com/paper/2505.02288/) (2025)
- [Confidence-Aware Learning for Camouflaged Object Detection](https://mlsanity.com/paper/2106.11641/) (2021)

## Abstract (arXiv)

Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large number of parameters. Non-Bayesian methods are simple to implement but often conflate different sources of uncertainties and require huge computing resources. We propose a new method for quantifying uncertainties of DNNs from a dynamical system perspective. The core of our method is to view DNN transformations as state evolution of a stochastic dynamical system and introduce a Brownian motion term for capturing epistemic uncertainty. Based on this perspective, we propose a neural stochastic differential equation model (SDE-Net) which consists of (1) a drift net that controls the system to fit the predictive function; and (2) a diffusion net that captures epistemic uncertainty. We theoretically analyze the existence and uniqueness of the solution to SDE-Net. Our experiments demonstrate that the SDE-Net model can outperform existing uncertainty estimation methods across a series of tasks where uncertainty plays a fundamental role.