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AI–aided design accelerates product development by computationally evaluating options starting with the desired end result.
In some ways, John von Neumann was a man ahead of his time. A gifted mathematician and physicist whose contributions to the Manhattan Project matched those of colleagues such as J. Robert Oppenheimer and Ernest O. Lawrence, von Neumann’s mathematical genius and his ability to apply it across scientific and technical domains makes him one of history’s most epic minds. In addition to providing the mathematical underpinnings for quantum physics and the study of game theory, von Neumann was a pioneer and visionary for the development of digital computing and its potential capabilities.
In the 1950s, as a commissioner for the United States Atomic Energy Commission—the Department of Energy’s (DOE’s) predecessor—von Neumann urged government leaders to establish a program that integrated applied mathematics and the most advanced computers of the day to evaluate scientific and technical challenges. His ideas for how computers could be used to model and understand multiphysics processes were both prescient and revolutionary. In his book, The Computer and the Brain, an unfinished work published posthumously, von Neumann was the first to suggest that a computer could exhibit “learned” behavior, improving its performance through experience. Nearly 70 years later, burgeoning advances in machine learning (ML) and AI are bringing this concept full circle, enabling ever-more powerful tools for investigation and discovery.

Like von Neumann, the founders of Lawrence Livermore recognized the immense utility of computers for solving large, complex scientific calculations. During its first year of operation, the Laboratory acquired the UNIVAC-1, which was followed in 1954 by the IBM 701. Based on what is known as the von Neumann architecture (a stored-program computer), the IBM 701 was the first commercially successful scientific supercomputer and paved the way for Livermore’s preeminence in the exploration, development, and acquisition of high-performance computers to promote physics understanding in support of its national security mission.
Building on this rich history and leveraging the Laboratory’s fastest and most powerful high-performance computing (HPC) systems, a multidisciplinary team of Livermore scientists and engineers embarked on an ambitious, three-year-long project beginning in 2021 to explore applications of AI and ML to scientific problems of complex hydrodynamics, shockwave physics, and energetic materials. Funded through the Laboratory Directed Research and Development (LDRD) Program, the DarkStar project has resulted in novel, AI-enabled simulation approaches that greatly accelerate physics and engineering design. “DarkStar’s genesis came from the confluence of many different ideas, some of which went back to John von Neumann,” says DarkStar principal investigator Jon Belof, who leads the program from within the Laboratory’s Physical and Life Sciences Principal Directorate. “He foresaw that compute power would reach a point where we could consider developing cognitive computational methods that operate similarly to how the brain functions and then use these methods to better understand complicated physical phenomena.”
As generative networks gain momentum, and the networks mature in capability, Belof and members of the DarkStar team reimagined how the most advanced computational tools of the modern age could be exploited to address pressing national needs. In doing so, the team created an entirely new AI-aided approach to time-dependent physics problems. Called inverse design, the technique enables researchers to discover optimized design solutions by starting from the desired outcome they want to achieve. “Demonstrating that complex systems can be developed directly from a final state and the initial design resolved by satisfying several constraints simultaneously via AI and machine learning enabled us to make several groundbreaking discoveries in the area of hydrodynamic instability,” says Belof. “Through extensive dynamics materials campaigns, we showed that these techniques help us understand this physical phenomena and allow us to control it.”
The Challenge of Dimensionality
As one of the three key pillars of scientific research, simulation works alongside the pillars of theory and experimentation to prove the realities of the natural world. In computational physics, the focus is historically on solving physics equations needed to simulate a process of interest over time. To solve these equations, computers perform time steps, many thousands of sequential calculations that move a system forward until the simulation terminates. As computers have advanced in speed and power, so have the accuracy of results, and researchers can now glean increasingly sophisticated data from simulations in vast research domains.
The DarkStar team posited that if they could harness this immense compute power differently—focusing less on the detailed physics and more on a system’s design space—they could develop new methods for accelerating scientific and engineering design for an equally vast number of applications. “Even with the most advanced computers available, we have finite computational power. To realize our design concepts, we needed to develop a different mode of computation and a framework for executing it,” says Belof. The DarkStar AI–ML-based inverse design framework efficiently uses HPC resources to systematically and rapidly probe massive (high-dimensional) design spaces, allowing scientists to resolve an initial design for a complex, time-dependent system by starting with the desired result they want to achieve.
Visualizing abstract, high-dimensional geometric spaces with, perhaps, 10 or more dimensions is difficult, but these objects can be defined mathematically and simulated computationally, with each dimension corresponding to specific features of an object. A drone, for instance, could be made to go faster by adjusting a feature such as its shape. Mathematical functions describe various shapes, yet the optimal functions depend on different variables and their unknown interactions. The more shapes considered, the more variables at play, and the more unknown interactions with physical forces, such as aerodynamic drag. As dimensions are added, the volume of a design space grows exponentially, and the regions of the space corresponding to useful designs become increasingly sparse. To overcome this issue, the DarkStar framework can be likened to a lamp, shining light on the darker regions of the design space by using machine learning to mathematically find the most important combinations of variables to create the desired design.
The DarkStar workflow begins by parameterizing the problem of interest. “The process is similar to an experimental analyst who helps devise a setup for an experiment to achieve some desirable response,” says Livermore computational engineer and DarkStar team member Charles Jekel. “An experimentalist may want to study a certain aspect of a test but may not know when to turn on the diagnostics, or how fast to shoot a projectile, or the best design for a target.” Parameterization sets up the computational geometry and finite element mesh that establishes the initial conditions for subsequent simulations. Finite element numerical methods provide efficient solvers for partial differential equations, which define processes in a rigorous mathematical form. (See S&TR, February 2021, The Exascale Software Portfolio.) Belof says, “We have points scattered within the design space, and each point corresponds to a different design. We then run tens of thousands of physics simulations in which we vary the initial conditions to determine the best performing candidates.” Using a Livermore-developed workflow tool called Merlin, the team can assemble, run, and process large-scale HPC workflows. Merlin manages the entire queuing system, job set up, and execution of tasks, including necessary restarts for simulation runs. Daniel White, a senior computational scientist at the Laboratory who led the simulation and AI team for DarkStar says, “When I started at the Laboratory 30 years ago, a single 2D simulation could take an entire week. With Merlin, we can orchestrate 10,000 simulations over the weekend and hundreds of thousands of simulations in a week.”

Notably, different modules can be used in this part of the framework depending on the needs of the study and the dimensionality of the problem. “We use a statistical method called Latin hypercubes to generate a random sample of parameter values. However, we’ve developed other, more intelligent sampling techniques,” says Belof. Taking a page out of Charles Darwin’s playbook, the team used a technique called differential evolution, which applies a “survival of the fittest” approach to refining a constraints-based design. The team can randomly sample and perturb certain variables, take the best performing ones, and then mutate them, perturbing their computational “genes” to create hundreds of mutant variations. Says Belof, “We then run simulations on each of those mutants and repeat the process until we obtain the optimal set of parameters for achieving a desired outcome, providing us with the best initial conditions for use in our hydrodynamic simulations.”
MARBL is a high-order arbitrary Lagrangian–Eulerian multiphysics code that subdivides systems into finite element space, yielding continuous mathematical functions in discrete components, enabling convergence on a solution. MARBL was started in 2016 as part of the Advanced Simulation and Computing (ASC) Advanced Technology Development and Mitigation program in collaboration with the DOE’s Exascale Computing Project. “As MARBL is a relatively new code, we highly value engagements with adventurous code users who help push the state of the art in simulation. Working with the DarkStar project was a rewarding and exciting experience for the code development team that helped us refine our simulation technology,” says MARBL project lead Rob Rieben.
Livermore’s tremendous work over the last few years on MARBL to make it run efficiently on faster, more powerful supercomputing architectures—particularly exascale systems—has drastically improved time to solution for simulating complex physics problems. MARBL can run on the Laboratory’s most advanced HPC systems, which are based on graphics processing units, and its resulting 2D and 3D simulations provide large data sets for training a generative learning model on hydrodynamic response. “We developed new machine-learning algorithms that take large ensembles of simulation results and sift through the data looking for patterns to help us determine what design variables are important,” says White. “The algorithms also enabled us to develop an entirely new compact surrogate model that captures all the interesting results of our simulations.” This surrogate model, based on generative AI technology, has become key to DarkStar’s design optimization success, allowing researchers to explore several facets of a design space in real time and facilitating cross-team collaboration.
The Intelligence of “PROFESSOR”
The thousands of MARBL physics simulation results from a parameterized problem generate terabytes of data. DarkStar’s AI-encoded ML model translates this massive amount of data into an adjustable, visualized representation of the physics. “At the beginning of DarkStar, we were working with an application for viewing large ensembles of simulation results,” says Jekel. “Simultaneously, I was fitting machine-learning models to learn the entire hydrodynamic field solutions for a parameterized problem so that it could predict at any place in time what the simulation results would look like. We put those two concepts together.”
The “brain” behind the model is a code called PROFESSOR, which provides an end-to-end functionality by integrating both the ML model and a graphical user interface. PROFESSOR takes the terabytes of simulation data, maps parameters to the full-field solutions, and then learns this mapping. Individual parameters, such as time, can be adjusted using “slider” bars that change the parameters independently. The simulated outcome is displayed in real time. “Every time a user moves a slider, the code queries the machine-learning model to recalculate the update,” says Jekel. Rather than being limited to the data on hand, the new software tool offers a significant benefit. “With PROFESSOR, users can adjust parameters and even visualize scenarios that weren’t simulated.”
The AI–ML model runs 10,000 times faster than the pure physics hydrodynamics simulations and compresses the terabytes of information into a few hundred megabytes, which makes the information easier to share among colleagues. White says, “This model provides us with a tremendous way to collaborate with others. We can email the file to users, and they can review all the simulations and explore the different parameters on their own. As a team, it helps us evaluate how sensitive the results are to the design variables, indicating which design variables are most important to a specific outcome.”
Controlling Instability

Through experimental campaigns conducted at facilities across the National Nuclear Security Administration (NNSA) complex, the team successfully verified its radical new AI–ML approach to predict new ways of tailoring complex material dynamics. In particular, the team investigated how their inverse design framework could be applied to better understand and control Richtmyer–Meshkov instabilities (RMI). RMI has implications in research spaces ranging from inertial confinement fusion (ICF)—an energy process that initiates nuclear fusion reactions by compressing and heating targets filled with fuel—to explosively driven shaped charges (meant to focus the effect of an explosive’s energy) used in the oil and gas industry. With the help of inverse design and access to additive manufacturing capabilities, the team made nonintuitive changes to concept designs, leading to improved experimental performance.
RMI is a type of fluid dynamics phenomena that occurs at a material interface. When materials of different densities experience shock loading (accelerated from a high-velocity impact), they run the risk of mixing at the point of contact, a process that can yield side effects that reduce performance. Jetting is one such side effect, wherein perturbations at the material interface grow into narrow spikes in which one material propagates into the other. “For DarkStar, our goal was to reduce RMI jetting behavior for certain design scenarios. We used gas-gun and high-explosives (HE) experiments to test our predictions,” says Dylan Kline, a Livermore HE expert who led the HE experiments for DarkStar. “Our AI model helped optimize designs for the desired results before conducting the tests.”

Gas-gun experiments modeled RMI events relevant to ICF. “We are simulating complicated physics, but we are also trying to control that complicated physics to achieve fusion,” says Will Schill, a design physicist who led the DarkStar gas-gun campaigns. “When a heavy material is placed right next to a light material and they are accelerated quickly with a shockwave, the tendency is for the heavy and the light materials to mix very rapidly via RMI, and those aren’t conducive conditions for fusion.”
Inverse design enables the team to evaluate how different engineering features, such as a material’s geometry, and time-dependent sources for delivering impulse load to the interface, can be used to manipulate RMI. “The ML model allowed us to represent the physics quickly and to query different aspects for the design, which, surprisingly, allowed us to gain insights into overall behavior,” says Schill. “The model indicates the direction of which physics design areas, such as the timing and shape of the shockwaves, we should consider first. It helps us answer if some kind of simple dynamics is being captured repeatedly that can guide us to a solution?” The team tested their designs on a single-stage gas gun at the Special Technologies Laboratory in Santa Barbara, California, and successfully demonstrated that when a heavy–light interface is loaded by two shocks in sequence, careful design of the shock sequence results in a near-perfect suppression of RMI growth. The experiments also paid dividends in understanding a unique, unexplored aspect of phase transitions in materials. “We found that in specific instances, a phase-transitioning material may self-suppress RMI, which was a surprising result.”
In another ICF-relevant gas-gun study led by Livermore engineer Dane Sterbentz, who also helped optimize the differential evolution technique for DarkStar, the research team simulated RMI jetting that occurs when a high-velocity impactor strikes a stationary target whose opposite side is exposed to air, and how changing the geometry of the impacted material could be used to suppress RMI spike growth. Differential evolution sampling was used to identify five parameters that are critical to reducing spike growth. The experiments conducted to test the optimized results demonstrated that RMI suppression can be achieved by implementing an optimized profile for the stationary target that counteracts spike growth at the material–air interface.
Kline, who produced design concepts for the HE experiments, notes that manufacturing processes for HE builds are an “entirely different beast.” He says, “For DarkStar, we had to develop tools, diagnostics, and methods to manufacture AI-generated linear shaped charge designs generated by the physicists. The tradeoff is that because machine learning is not accounting for a design’s manufacturability, the results can be impossible to realize physically. Machine learning has no knowledge of, for example, whether a design would be easy or hard to make, it just says ‘this is the best result.’ Additive manufacturing gives us the flexibility to makes those unique designs.”
Using the DarkStar framework and the Laboratory’s 3D printing capabilities, the team demonstrated how their new methodologies can rapidly develop and experimentally validate modifications to linear shaped charges. One study’s framework provided an optimized set of conditions for reducing RMI evolution in explosively driven linear shaped charge designs using a copper liner, an HE, and a silicone buffer. The experiments compared a baseline design, which did not use a buffer between the liner and the HE, against a design with the computationally optimized silicon component. Flash x-ray radiographs taken during the detonation experiments revealed the silicone buffer’s ability to mitigate potential instabilities reliably and consistently. The team conducted a total of 14 HE detonation experiments at Livermore’s High Explosive Applications Facility (HEAF) comparing multiple methods to modify RMI, including buffers, liner modifications, multiple HEs, and specially sequenced shocks.

Separately, the DarkStar AI–ML approach featured prominently in work to improve the jet characteristics of these devices. The neural network was fit to the multiphysics simulations to create the surrogate model, enabling users to interactively assess the performance of various designs for modifying jet formation. The HEAF team provided shaped charge assemblies with complicated, AI-generated geometries for the experiments. “We produced a linear shaped charge design with a higher penetration depth than a baseline case using the same amount of or less HE,” say White. “Generally, we think more explosive is better, but we came up with designs that use less explosive to make the overall device work better.”
Through their series of experiments, the team has uncovered several groundbreaking discoveries regarding hydrodynamic instabilities, including how to completely suppress RMI under various conditions. “The work we’ve done with DarkStar is not just about better designs, but more importantly the speed at which we can deliver them,” says White. “Our inverse design approach enables rapid turnaround, not the years or decades it took previously.” This work was further expedited by having the talent, tools, and expertise at the Laboratory to turn designs into physical concepts that could then be tested. Kline adds, “Each of our designs went through optimization, manufacturing, and detonation testing in less than three months.” The team’s achievements are an exceptional story of success, and one that is just beginning.
An All-Around Win
The DarkStar project is an exemplar of the immense power of multidisciplinary teams working toward achieving ambitious goals (see sidebar below). Schill says, “We are fortunate to have had computational physicists, engineers, and experimentalists working collaboratively to realize optimized designs, turn those designs into actual builds, and then test and verify that the designs were a success.” The team’s work has delivered scientific breakthroughs and new computational capabilities and has shown that projects such as DarkStar are critical to the Laboratory’s future workforce pipeline.
The Mozart of Science and Technology
Johnny Foster, Jr., has been a tour de force for national security. A brilliant design physicist, team leader, Lawrence Livermore National Laboratory director, and former director of Defense Research and Engineering at the Department of Defense, Foster challenged the Laboratory to remain a place where multidisciplinary teams can explore complicated, daring, and risky goals for the good of the nation and the world. He championed creative science with attendant detailed engineering, and the importance of intense technical questioning and peer review for verifying technical validity.

At 102 years old, Foster continues to push generations of succeeding scientists and engineers to take risks and expand their scientific horizons. As part of the DarkStar effort, Livermore physicist Jon Belof and others met with Foster several times over the three-year project to gain insight and seek his recommendations on goals and deliverables. “Imagine being able to give Mozart an electric guitar and say, ‘what would you do with this?’” says Belof. Foster, in a way, is the Mozart of science and technology, offering his extensive expertise to merge past and present ideas to achieve ambitious goals for the future. “We have new technologies, such as artificial intelligence and machine learning, that didn’t exist 50 to 70 years ago. We wanted to know how he would have used these technologies if he had had them in the founding days of the Laboratory. He would advise, give us homework, expect an update, and provide feedback.”
For early career design physicist Will Schill, the opportunity to meet Foster provided a unique perspective on how to tackle the Laboratory’s important work. “One of the biggest takeaways meeting Johnny was the idea that if we can truly understand what the nation needs in terms of national security, and we can aggressively go after that goal and be willing to accept risk and do things that are potentially different than maybe how things were done, or how others think they should be done, we can make a huge difference.”
Foster’s remarkable ability to inspire, mentor, and motivate his colleagues are attributes honored by the John S. Foster Jr. Medal, which is administered by Lawrence Livermore National Security, LLC, annually to recognize innovative and inspirational leadership in national security. Belof says, “We learned from Johnny that we have to be ambitious—maybe the ideas work, maybe they don’t—but it is our duty to try, and we can’t rest on laurels. Innovation in science and technology is our national mandate.”
Several team members, mentored by senior Laboratory staff, started on the project as postdoctoral researchers and are now full-time staff. The project has also provided an opportunity to collaborate with students at universities across the country, including the Colorado School of Mines in Golden, Colorado. Kline, who led the collaboration, says, “The school has extensive experience with energetics and a test facility that we helped revitalize for possible future testing. This work supports students who have energetic materials experience coming to the Laboratory, and we can share our knowledge of 3D printing.” These essential external collaborations resulted in more than 30 publications for the DarkStar project. Additional university collaborators included Cornell University, the Massachusetts Institute of Technology, the University of California (UC) at Davis, and UC San Diego, among others.
Going forward, DarkStar has realized world-leading, advanced AI technology that will support Livermore’s pursuit of current and future mission areas and enable NNSA programs. Livermore’s people, expertise, advanced physics codes, exploration of AI techniques, and access to HPC platforms make the Laboratory uniquely suited to carry on this work. White says, “The design problems we are tackling are extremely difficult. The physics is complicated, and no simple analytical approximations can be applied that are useful for these problems. We couldn’t have done this work without our talented team and the Laboratory’s supercomputing capabilities.” Incidentally, the DarkStar project was one of the largest users of the Laboratory’s compute resources over the last three years through allocations provided by the ASC Advanced Technology Computing Campaign.
In 2024, the Laboratory welcomed its newest HPC system for NNSA with the delivery of the agency’s first exascale machine—El Capitan. The system can run the highest resolution 3D simulations of multiphysics codes possible to date and brings a new level of confidence and efficiency to national security missions. White says, “We are excited about running our AI-enabled model on El Capitan because we can run 10 times as many simulations in more detail, which allows us to explore even larger design spaces.
“El Capitan will continue to revolutionize how we execute design using AI.” Belof adds, “The Laboratory is uniquely suited to develop these types of advanced tools that will dramatically change our productivity and outcomes. Our leadership in HPC and advanced simulation positions the Laboratory well to make the next breakthroughs in AI. DarkStar is the start of things to come.” Building on history and looking toward the future, the DarkStar team has shown that the world will soon see the lasting import of von Neumann’s genius.
—Caryn Meissner
For further information contact Jon Belof (925) 424-1399 (belof1 [at] llnl.gov (belof1[at]llnl[dot]gov)).