### High-Consequence Research & Education

#### The Oden Institute is tackling the challenges of Predictive Data Science across high-consequence applications in science, engineering and medicine.

# Big decisions need more than just big data

## They need big models too.

Today's high-consequence decisions in engineering, science and medicine need methods based on more than just data analytics. These decisions must incorporate the predictive power, interpretability and domain knowledge of physics-based models. Enter Predictive Data Science.

## Whitepaper

### The shortcomings of data science for high-consequence decisions

High-consequence decisions in science, engineering and medicine are almost always based on predictions that go beyond the available data. We often need to make predictions about a future state — about the future state of a patient's illness, about the states that an engineering system may find itself experiencing in operation, or about the future state of the Earth's climate in the decades to come. In these settings, there are multiple reasons that pure-data machine learning and statistical approaches will struggle to generalize with high confidence:

The applications are characterized by complex multiscale multiphysics dynamics, so that small changes in parameters can lead to large changes in system behavior.

The parameter space is very high dimensional. Many parameters of interest are fields (infinite dimensional). Without the constraints of physics, the solution space is so vast that driving decisions with data alone is doomed to failure.

Data are sparse and typically rely on physical sensing infrastructure, making them expensive to acquire. Data may be large in volume, but they provide only limited peeks into the underlying high-dimensional parameter space.

Uncertainty quantification of predictions must provide quantified confidence in the recommended decisions. This is especially challenging but especially important as we extrapolate beyond the data to issue predictions about future states.

### Predictive Data Science — A new convergence

What is Data Science?

Data science is a multi-disciplinary field that uses scientific methods, processes, algorithms and systems to extract knowledge and insights from structured and unstructured data. [Wikipedia]

What is Computational Science & Engineering?

Computational Science & Engineering (CSE) is an interdisciplinary field that uses mathematical modeling and advanced computing to solve complex problems. In CSE, we develop models and simulations to understand physical and natural systems. [Wikipedia]

What is **Predictive Data Science**?

Predictive Data Science is the convergence of Data Science and Computational Science & Engineering. Predictive Data Science integrates physics-based models **and** data to tackle the challenges of high-consequence decisions across science, engineering and medicine.

Respect physical constraints

Embed domain knowledge

Bring interpretability to results

Integrate heterogeneous, noisy & incomplete data

Get predictions with quantified uncertainties

Guide optimal data acquisition strategies

Watch a video explanation of Predictive Data Science at ICIAM 2019.

### What is a physics-based model?

What is a physics-based model?

A physics-based model incorporates governing principles and laws of nature. These laws of nature define how physical, chemical and biological processes evolve.

These laws of nature typically appear in physics-based models as systems of differential equations.

How do you work with these equations?

You need numerical methods. These numerical methods discretize the governing differential equations, resulting in numerical models that are large-scale systems of equations. With high-performance computing, we solve these numerical models to determine the solutions.

Why are physics-based models so useful?

The numerical models are parameterized with many, many parameters, representing system properties such as geometry, material properties, initial conditions, boundary conditions, and more. Thus, the numerical model is a valuable tool for exploring "what-if" questions — What if we apply this treatment? What if we choose this shape for the aircraft wing? — all informed by predictions that respect the laws of nature.

### The Unreasonable Effectiveness of physics-based predictions

Why are physics-based models predictive?

Because in solving the governing equations of the system, they constrain the predictions to lie on the solution manifold defined by the laws of nature.

Is it easy to combine data with physics-based models?

No — these models usually manifest as high-dimensional computational models that take hours or weeks to simulate.

**But**, this is where modern techniques of CSE come in — techniques that exploit structure, discover low-dimensional approximations, and leverage high-performance computing. Explore just a few such techniques below:

### What's next: The future of Predictive Data Science

Big

across science, engineering & medicine need Predictive Data Science.

need new scalable methods for learning from data through the lens of physics-based models.

need scalable uncertainty quantification that targets certified predictions in support of decision.

need students trained at the interfaces of computer science, mathematics, statistics, high performance computing, and applications across science, engineering and medicine.

The

Oden

conducts cutting-edge interdisciplinary research and education to tackle these challenges.

is addressing science, engineering & medicine grand challenges through new methods, scalable algorithms & high-performance computing.

is advancing the architecture–algorithm–application nexus to transform next-generation computational science.

is building the mathematical & statistical foundations for predictive science, data science & machine learning.

leads the world in interdisciplinary education at the interfaces of computer science, mathematics, statistics, high performance computing, and applications across science, engineering and medicine.

Learn more at www.oden.utexas.edu