# Posts by Collection

## portfolio

## publications

## Advanced Fluid Reduced Order Models for Compressible Flow

Published in *Sandia National Laboratories Report, Sand No. 2017-10335*, 2017

*Chapter 5: Structure preservation in finite volume ROMs via physics-based constraints*

Recommended citation: Tezaur, I.K., Fike, J., Carlberg, K., Barone, M., **Maddix, D.C.**, Mussoni, E., Balajewicz, M. (2017). "Advanced Fluid Reduced Order Models for Compressible Flow." *Sandia National Laboratories Report, Sand No. 2017-10335*. __https://www.osti.gov/servlets/purl/1395816__

## Numerical Artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

Published in *Journal of Computational Physics*, 2018

Recommended citation: **Maddix, D.C.**, Sampaio, L., Gerritsen, M. (2018). "Numerical Artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame." *Journal of Computational Physics*. 361:280-298. __https://arxiv.org/abs/1709.02581__

## Numerical Artifacts in the discontinuous Generalized Porous Medium Equation: How to avoid spurious temporal oscillations

Published in *Journal of Computational Physics*, 2018

Recommended citation: **Maddix, D.C.**, Sampaio, L., Gerritsen, M. (2018). "Numerical Artifacts in the discontinuous Generalized Porous Medium Equation: How to avoid spurious temporal oscillations." *Journal of Computational Physics*. 368:277-298. __https://arxiv.org/abs/1712.00132__

## Deep Factors for Forecasting

Published in *Proceedings of the 36th International Conference on Machine Learning (ICML)*, 2019

Our Deep Factor code is in GluonTS.

Recommended citation: Wang, Y., Smola, A., **Maddix, D.C.**, Gasthaus, J., Foster, D. (2019). "Deep Factors for Forecasting." *Proceedings of the 39th International Conference on Machine Learning (ICML), PMLR*. 97:6607-6617. __http://proceedings.mlr.press/v97/wang19k/wang19k.pdf__

## GluonTS: Probabilistic and Neural Time Series Modeling in Python

Published in *Proceedings of the 39th International Conference on Machine Learning (ICML)*, 2020

Recommended citation: Alexandrov, A., Benidis, K., Bohlke-Schneider, M., Flunkert, V., Gasthaus, J., Januschowski, T., **Maddix, D.C.**, Rangapuram, S., Salinas, D., Schulz, J., Stella, L., Türkmen, A.C., Wang, Y. (2020). "GluonTS: Probabilistic and Neural Time Series Modeling in Python." *Journal of Machine Learning Research (JMLR)*. 21(116):1-6. __https://www.jmlr.org/papers/v21/19-820.html__

## Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems

Published in *Proceedings of the 3rd Conference on Learning for Dynamics and Control (L4DC)*, 2021

Our AutoODE code is on github.

Recommended citation: Wang, R., **Maddix, D.C.**, Faloutsos, C., Wang, Y., Yu, R. (2021). "Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems." *Proceedings of the 3rd Conference on Learning for Dynamics and Control (L4DC), PMLR.* 144:385-398. __http://proceedings.mlr.press/v144/wang21a/wang21a.pdf__

## Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting

Published in *Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS)*, 2022

Our Incremental Quantile Function (IQF) code is incorporated into the MQ-CNN Estimator in GluonTS.

Recommended citation: Park, Y., **Maddix, D.C.**, Aubet, FX., Kan, K., Gasthaus, J., Wang, Y. (2022). "Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting." *Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR.* 151:8127-8150. __https://proceedings.mlr.press/v151/park22a.html__

## Domain Adaptation for Time Series Forecasting via Attention Sharing

Published in *Proceedings of the 39th International Conference on Machine Learning (ICML)*, 2022

Recommended citation: Jin, X., Park, Y., **Maddix, D.C.**, Wang, H., Wang, Y. (2022). "Domain Adaptation for Time Series Forecasting via Attention Sharing." *Proceedings of the 39th International Conference on Machine Learning (ICML), PMLR*. 162:10280-10297. __https://proceedings.mlr.press/v162/jin22d/jin22d.pdf__

## Deep Learning For Time Series Forecasting: Tutorial and Literature Survey

Published in *ACM Computing Surveys*, 2022

Recommended citation: Benidis, K., Rangapuram, S., Flunkert V., Wang, Y., **Maddix, D.C.**, Türkmen, C., Gasthaus, J., Bohlke-Schneider, M., Salinas, D., Stella, L., Aubet, FX., Callot, L, Januschowski, T. (2022). "Deep Learning for Time Series Forecasting: Tutorial and Literature Survey." *ACM Computing Surveys*. 55(6):1-36. __https://arxiv.org/pdf/2004.10240__

## Guiding Continuous Operator Learning through Physics-based boundary constraints

Published in *Proceedings of the International Conference on Learning Representations (ICLR)*, 2023

Our Boundary enforcing Operator Network (BOON) code is on the amazon-science github.

Recommended citation: Saad, N.*, Gupta, G.*, Alizadeh, S., **Maddix, D.C.** (2023). "Guiding Continuous Operator Learning through Physics-based boundary constraints." *Proceedings of the International Conference on Learning Representations (ICLR)*. __https://www.amazon.science/publications/guiding-continuous-operator-learning-through-physics-based-boundary-constraints__

## Theoretical Guarantees of Learning Ensembling Strategies with Applications to Time Series Forecasting

Published in *Proceedings of the 40th International Conference on Machine Learning (ICML)*, 2023

Recommended citation: Hasson, H., **Maddix, D.C.**, Wang, Y., Park, Y., Gupta, G., (2023). "Theoretical Guarantees of Learning Ensembling Strategies with Applications to Time Series Forecasting." *Proceedings of the 40th International Conference on Machine Learning (ICML), PMLR*. 202:12616-12632. __https://proceedings.mlr.press/v202/hasson23a/hasson23a.pdf__

## Learning Physical Models that Can Respect Conservation Laws

Published in *Proceedings of the 40th International Conference on Machine Learning (ICML)*, 2023

Recommended citation: Hansen, D., **Maddix, D.C.**, Alizadeh, S., Gupta, G., Mahoney, M.W. (2023). "Learning Physical Models that Can Respect Conservation Laws." *Proceedings of the 40th International Conference on Machine Learning (ICML), PMLR*. 202:12469-12510. __http://proceedings.mlr.press/v202/hansen23b/hansen23b.pdf__

## PreDiff: Precipitation Nowcasting with Latent Diffusion Models

Published in *Proceedings of the 37th Conference of Neural Information Processing Systems (NeurIPS)*, 2023

Our PreDiff code is available on github.

Recommended citation: Gao, Z., Shi, X., Han, B., Wang, H., Jin, X., **Maddix, D.C.**, Zhu, Y., Li, M., Wang, Y. (2023). "PreDiff: Precipitation Nowcasting with Latent Diffusion Models." *Proceedings of the 37th Conference of Neural Information Processing Systems (NeurIPS)*. __https://proceedings.neurips.cc/paper_files/paper/2023/file/f82ba6a6b981fbbecf5f2ee5de7db39c-Paper-Conference.pdf__

## Learning Physical Models that Can Respect Conservation Laws

Published in *Physica D: Nonlinear Phenomena*, 2024

Our ProbConserv code is on the amazon-science github.

Recommended citation: Hansen, D.*, **Maddix, D.C.***, Alizadeh, S., Gupta, G., Mahoney, M.W. (2024). "Learning Physical Models that Can Respect Conservation Laws." *Physica D: Nonlinear Phenomena, 457 (133952)*, (*Equal contributions). __https://doi.org/10.1016/j.physd.2023.133952__

## Machine Learning for Road Vehicle Aerodynamics Simulation

Published in *Society of Automotive Engineers (SAE) Technical Paper*, 2024

Recommended citation: Ananthan, V., Ashton, N., Chadwick, N., Lizarraga, M., **Maddix, D.C.**, et al. (2024). "Machine Learning for Road Vehicle Aerodynamics Simulation." *Society of Automotive Engineers (SAE) Technical Paper*. __https://www.sae.org/publications/technical-papers/content/2024-01-2529/__

## Chronos: Learning the Language of Time Series

Published in *Technical Report, Preprint arXiv:2403.07815*, 2024

Our Chronos code is on the amazon-science github.

Recommended citation: Ansari, F.A., Stella, L., Turkmen, C., Zhang, X., Mercado, P., Shen, H., Shchur, O., Rangapuram, S.S., Arango, S.A., Kapoor, S., Zschiegner, J., **Maddix, D.C.**, et al. (2024). "Chronos: Learning the Language of Time Series." * Technical Report, Preprint arXiv:2403.07815*. __https://arxiv.org/abs/2403.07815__

## Transferring Knowledge from Large Foundation Models to Small Downstream Tasks

Published in *Proceedings of the 41st International Conference on Machine Learning (ICML)*, 2024

Recommended citation: Qiu, S., Han, B, **Maddix, D.C.**, Zhang, S., Wang, Y., Wilson, A.G. (2024). "Transferring Knowledge from Large Foundation Models to Small Downstream Tasks." *Proceedings of the 41st International Conference on Machine Learning (ICML), PMLR.* 235. __https://arxiv.org/abs/2406.07337__

## Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs

Published in *Proceedings of the 41st International Conference on Machine Learning (ICML)*, 2024

Our Operator-ProbConserv code is on the amazon-science github.

Recommended citation: Mouli, S.C., **Maddix, D.C.**, Alizadeh, S., Gupta, G., Wang, Y., Stuart, A., Mahoney, M.W. (2024). "Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs." *Proceedings of the 41st International Conference on Machine Learning (ICML), PMLR.* 235. __https://arxiv.org/abs/2403.10642__

## Comparing and Contrasting Deep Learning Weather Prediction Backbones on Navier-Stokes and Atmospheric Dynamics

Published in *Technical Report, Preprint arXiv:2407.14129*, 2024

Shorter version on Navier Stokes dynamics accepted at the ICLR 2024 Workshop on AI4DifferentialEquations In Science.

Recommended citation: Karlbauer, M., **Maddix, D.C.**, Ansari, A.F., Han, B., Gupta, G., Wang, Y., Stuart, A., Mahoney, M.W., (2024). "Comparing and Contrasting Deep Learning Weather Prediction Backbones on Navier-Stokes and Atmospheric Dynamics." * Technical Report, Preprint arXiv:2407.14129*. __https://arxiv.org/abs/2407.14129__

## talks

## ICME Xpo Research Symposium

** Published:**

I presented posters on my research at the ICME Xpo Research Symposium from 2015-2018 on the following topics:

- Numerical Artifacts in the Generalized Porous Medium Equation and Solutions,
*PhD Thesis Research*, 2017-2018 - Sparse Matrix Vector Multiplication Using the Merge Path,
*NVIDIA*, 2016- Won the ICME Xpo Best Poster Presenter Award

- Applications of the Voronoi Implicit Interface Method for Shape Optimization Problems Involving Interconnected Regions,
*Lawrence Berkeley National Laboratory*, 2015

## Temporal oscillations in the porous medium equation: why harmonic averaging itself is not to blame

** Published:**

PhD Thesis Research on finite-volume averaged-based methods for nonlinear porous media flow

## Neural Time Series Models with GluonTS

** Published:**

ICML Time Series Workshop Talk with corresponding youtube link on GluonTS.

## Mathematics in Science

** Published:**

Please find my talk here.

## Physics-constrained Machine Learning for Scientific Computing

** Published:**

My invited talk on “Physics-constrained Machine Learning for Scientific Computing” at the Machine Learning and Dynamical Systems Seminar at the Alan Turing Institute covers our following three research works:

## Women in Science at Amazon: A Conversation with our Amazonians Panelists

** Published:**

In this panel, we discuss challenges for women in STEM and how to persevere, internship mentoring opportunities and the future uses of machine learning in science.

## Physics-constrained Machine Learning for Earth and Sustainability Science

** Published:**

My talk on “Physics-constrained Machine Learning for Earth and Sustainability Science” at the 2nd AI for Good Webinar Series for AI for Earth and Sustainability Science covers our following four research works in various scientific disciplines from epidemiology to weather and climate:

- Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems, L4DC, 2021.
- Learning Physical Models that Can Respect Conservation Laws, Physica D: Nonlinear Phenomena, 2024, ICML, 2023.
- Guiding Continuous Operator Learning through Physics-based boundary constraints, ICLR, 2023.
- PreDiff: Precipitation Nowcasting with Latent Diffusion Models, NeurIPS, 2023.

## Physics-constrained Machine Learning for Scientific Computing

** Published:**

I gave a guest lecture in Professor Krishnapriyan’s advanced Computer Science 294 graduate course on Physics Inspired Deep Learning at the University of California, Berkeley.

## Advances in Scientific Machine Learning (SciML) in Industry

** Published:**

I gave an invited talk at the Institute for Computational and Experimental Research in Mathematics (ICERM)’s Workshop on the Industrialization of SciML at Brown University.

## Physics-constrained Machine Learning for Scientific Computing

** Published:**

I will be giving an invited talk at the 2nd ICML Workshop on the Synergy of Scientific Machine Learning Modeling (SynS & ML).

## teaching

## Undergraduate Student Instructor (UGSI) for Math 16B, 54, 1B

Undergraduate course, *University of California, Berkeley*, 2011

I was one of a few undergraduate student instructors selected in the University of California, Berkeley’s mathematics department from 2011-2012.

## Lecturer for Math 54: Linear Algebra and Differential Equations, University of California, Berkeley

Undergraduate course, *University of California, Berkeley*, 2012

I taught the undergraduate Math 54 course at the University of California, Berkeley.

## ICME Numerical Linear Algebra Refresher Course

Graduate course, *Institute of Computational and Mathematical Engineering (ICME), Stanford University*, 2015

I taught the Numerical Linear Algebra ICME refresher course for incoming ICME graduate students to help them prepare for their first year core graduate courses.

## ICME Data Science Summer Workshop Instructor and Organizer

Professional and student course, *Institute of Computational and Mathematical Engineering, Stanford University*, 2016

I was the organizer of the 2016 ICME Data Science Workshops, which covered the fundamentals of data science for Stanford students and professionals in industry. I was also the instructor of the Advanced MATLAB workshop.

## CME 292 Advanced MATLAB for Scientific Computing

Graduate course, *Stanford University*, 2016

I taught and developed an Advanced MATLAB course aimed for graduate student scientists and engineers, covering topics including data structures, memory management, advanced graphics in higher dimensions, code optimization and debugging, object-oriented programming, compiled MATLAB (MEX files and MATLAB coder), and optimization, parallel computing, symbolic math and PDEs toolboxes.

## Machine Learning University (MLU): Accelerated Time Series Forecasting

Professional course, *Amazon Web Services (AWS)*, 2022

I taught and developed the materials for a course on operational time series forecasting covering classical local state space models, e.g., ARIMA and ETS and deep learning models, e.g., DeepAR. In addition, we covered how to use the GluonTS time series toolkit.

## ICME Data Science Summer Workshop Introduction to Statistics Instructor

Professional and student course, *Institute of Computational and Mathematical Engineering, Stanford University*, 2023

I taught the Introduction to Statistics course at the 2023 ICME Summer Workshops Fundamentals of Data Science, which covers the fundamentals of data science for Stanford students and professionals in industry internationally.