for computational nuclear data

LA-UR-21-30576

*IAEA AI4Atoms Workshop*

Monday October 25$^{th}$ 2021

Nuclear Data Team

Theoretical Division

**Los Alamos National Laboratory Caveat**

The submitted materials have been authored by an employee or employees of Triad National Security, LLC (Triad) under contract with the U.S. Department of Energy/National Nuclear Security Administration (DOE/NNSA).

Accordingly, the U.S. Government retains an irrevocable, nonexclusive, royaltyfree license to publish, translate, reproduce, use, or dispose of the published form of the work and to authorize others to do the same for U.S. Government purposes.

Example: fission yields are needed for a variety of applications and cutting-edge science

**Industrial applications:** simulation of reactors, fuel cycles, waste management

**Experiments:** backgrounds, isotope production with radioactive ion beams (fragmentation)

**Science applications:** nucleosynthesis, light curve observations

**Other Applications:** national security, nonproliferation, nuclear forensics

Figure: Chi-Nu detector (left), Reactor cooling towers (middle), Neutron star merger (right)

When we model nuclear data we think of it as a 'forward' problem

We start with our model and parameters and try to match measurements / observations

This is an extremely successful approach and is precisely how nuclear theory modeling for nuclear data works

**Mathematically:** $f(\vec{\boldsymbol{x}}) = \vec{\boldsymbol{y}}$

Where $f$ is our model, $\vec{\boldsymbol{x}}$ are the parameters for the model and $\vec{\boldsymbol{y}}$ are the predictions

Figure by **Mumpower**

There can be many challenges with this approach

For instance, how do we update our model if we don't match data?

*This can be challenging*

We don't always know what modifications are required or the physics could be very hard if not impossible to model given current computational limitations (e.g. many-body problem)

Treating this as an 'inverse problem' provides an alternative approach...

Figure by **Mumpower**

Suppose we start with the nuclear data (and its associated uncertainties)

We can then try to figure out what models may match relevant observations

This approach allows us to *vary* and optimize *the model*!

**Mathematically, still:** $f(\vec{\boldsymbol{x}}) = \vec{\boldsymbol{y}}$; but we want to now find $f$; fixing $\vec{\boldsymbol{x}}$

Machine learning and artificial intelligence algorithms are ideal for this class of problems...

Figure by **Mumpower**

My son Zachary has been very keen on learning his letters from an early age

Letters are well known (this represents the data we want to match to)

But the model (being able to draw - eventually letters) must be developed, practiced and finally optimized

This is a complex, iterative process - it takes times to find '$f$'!

Example from 1 years old; random drawing episode; time taken: 10 minutes

Drawing by Z. R. Mumpower

Example from 2.5 years old; first ever attempt to draw letters / alphabet; time taken: 2 hours!

Drawing by Z. R. Mumpower

Example from 3.5 years old; drawing scenery; time taken: 10 minutes

Drawing by Z. R. Mumpower

Example from 4 years old; tracing the days of the week; time taken: 30 minutes

Drawing by Z. R. Mumpower

A relatively easy choice is a scalar property; how about atomic binding energies (masses)?

Recall: $f(\vec{\boldsymbol{x}}) = \vec{\boldsymbol{y}}$

$f$ will be a neural network (a model that can change)

$\vec{\boldsymbol{y}_{obs}}$ are the observations (e.g. Atomic Mass Evaluation) we want to match $\vec{\boldsymbol{y}}$ with

But what about $\vec{\boldsymbol{x}}$?

Why not a *physically motivated* feature space!?

proton number ($Z$), neutron number, ($N$), nucleon number ($A$), etc.

This is a **completely different approach** than past work

Past work relies on matching model residuals: $\vec{\boldsymbol{y}}$ = (model output) - data

Why not use data as data, rather than mixing model output and data!? (this is difficult to interpret and understand)

Lovell, Mohan, Sprouse & **Mumpower** submitted (2021)

We use a variety of possible physically motivated features as inputs into the model

Lovell, Mohan, Sprouse & **Mumpower** submitted (2021)

**We take a Bayesian approach:** our network inputs are sampled based on nuclear data uncertainties

Our network outputs are therefore **statistical**

We can represent outputs by a collection of Gaussians (for masses we only need 1)

Our network therefore, also provides a quanitfied estimate of uncertainty (fully propagated through the model)

Lovell, Mohan, Sprouse & **Mumpower** submitted (2021)

Here we show results along the lead (Pb) [$Z=82$] isotopic chain

Data from the Atomic Mass Evaluation (AME2016) in black stars

Increasing sophistication of the model feature space indicated by M##

Lovell, Mohan, Sprouse & **Mumpower** submitted (2021)

Results across the chart of nuclides with increasing feature space complexity

Note the decrease in the maximum value of the scale

Lovell, Mohan, Sprouse & **Mumpower** submitted (2021)

A summary of results

**Some lessons learned:**

More physics added to the feature space → the better our description of atomic masses

Attempting to fit and predict other mass related quantities (e.g. separation energies) does impact our results (although marginal compared to choice of feature space)

We do not need deep neural networks to describe atomic masses; nor for extrapolations!

Lovell, Mohan, Sprouse & **Mumpower** submitted (2021)

My collaborators

A. Lovell, A. Mohan, & T. Sprouse

▣ Postdoc

And to my son Zachary for the use of his drawings

We are entering the era of computational nuclear data

**Recent advances:**

Los Alamos is developing a state-of-the-art computational nuclear data framework

This framework can combine measurements, observations and theoretical modeling to produce nuclear data with well-defined uncertainties that can be easily interpreted and shared with the community

As an example, we showed in this talk binding energies of atomic nuclei with a Bayesian neural network

Our methods are general and can be applied to any physical quantity or system

Results / Data / Papers **@** MatthewMumpower.com